[{"oa_version":"Preprint","abstract":[{"text":"We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.","lang":"eng"}],"month":"01","intvolume":" 63","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2012.15238","open_access":"1"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"publication_status":"published","volume":63,"issue":"1","ec_funded":1,"_id":"10600","status":"public","keyword":["mathematical physics","statistical and nonlinear physics"],"type":"journal_article","article_type":"original","date_updated":"2023-08-02T13:44:32Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"acknowledgement":"J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331.","quality_controlled":"1","publisher":"AIP Publishing","oa":1,"day":"03","publication":"Journal of Mathematical Physics","isi":1,"year":"2022","doi":"10.1063/5.0051632","date_published":"2022-01-03T00:00:00Z","date_created":"2022-01-03T12:19:48Z","article_number":"011901","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics, vol. 63, no. 1, 011901, AIP Publishing, 2022, doi:10.1063/5.0051632.","apa":"Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0051632","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 2022;63(1). doi:10.1063/5.0051632","short":"S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap,” Journal of Mathematical Physics, vol. 63, no. 1. AIP Publishing, 2022.","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0051632.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901."},"title":"Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"last_name":"Teufel","full_name":"Teufel, Stefan","first_name":"Stefan"}],"external_id":{"isi":["000739446000009"],"arxiv":["2012.15238"]},"article_processing_charge":"No"},{"title":"Local stability of ground states in locally gapped and weakly interacting quantum spin systems","author":[{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"first_name":"Stefan","last_name":"Teufel","full_name":"Teufel, Stefan"},{"full_name":"Wessel, Tom","last_name":"Wessel","first_name":"Tom"}],"external_id":{"arxiv":["2106.13780"],"isi":["000744930400001"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Henheik SJ, Teufel S, Wessel T. 2022. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 112(1), 9.","chicago":"Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s11005-021-01494-y.","ieee":"S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states in locally gapped and weakly interacting quantum spin systems,” Letters in Mathematical Physics, vol. 112, no. 1. Springer Nature, 2022.","short":"S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).","ama":"Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. 2022;112(1). doi:10.1007/s11005-021-01494-y","apa":"Henheik, S. J., Teufel, S., & Wessel, T. (2022). Local stability of ground states in locally gapped and weakly interacting quantum spin systems. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-021-01494-y","mla":"Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” Letters in Mathematical Physics, vol. 112, no. 1, 9, Springer Nature, 2022, doi:10.1007/s11005-021-01494-y."},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"article_number":"9","date_published":"2022-01-18T00:00:00Z","doi":"10.1007/s11005-021-01494-y","date_created":"2022-01-18T16:18:25Z","day":"18","publication":"Letters in Mathematical Physics","has_accepted_license":"1","isi":1,"year":"2022","quality_controlled":"1","publisher":"Springer Nature","oa":1,"acknowledgement":"J. H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond” No. 101020331. S. T. thanks Marius Lemm and Simone Warzel for very helpful comments and discussions and Jürg Fröhlich for references to the literature. Open Access funding enabled and organized by Projekt DEAL.","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-19T09:41:14Z","ddc":["530"],"date_updated":"2023-08-02T13:57:02Z","status":"public","keyword":["mathematical physics","statistical and nonlinear physics"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"10642","volume":112,"issue":"1","ec_funded":1,"file":[{"date_created":"2022-01-19T09:41:14Z","file_name":"2022_LettersMathPhys_Henheik.pdf","creator":"cchlebak","date_updated":"2022-01-19T09:41:14Z","file_size":357547,"file_id":"10647","checksum":"7e8e69b76e892c305071a4736131fe18","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"publication_status":"published","month":"01","intvolume":" 112","oa_version":"Published Version","abstract":[{"text":"Based on a result by Yarotsky (J Stat Phys 118, 2005), we prove that localized but otherwise arbitrary perturbations of weakly interacting quantum spin systems with uniformly gapped on-site terms change the ground state of such a system only locally, even if they close the spectral gap. We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences.","lang":"eng"}]},{"oa_version":"Published Version","abstract":[{"text":"We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n","lang":"eng"}],"month":"01","intvolume":" 10","file":[{"success":1,"checksum":"87592a755adcef22ea590a99dc728dd3","file_id":"10646","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2022_ForumMathSigma_Henheik.pdf","date_created":"2022-01-19T09:27:43Z","creator":"cchlebak","file_size":705323,"date_updated":"2022-01-19T09:27:43Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2050-5094"]},"publication_status":"published","volume":10,"ec_funded":1,"_id":"10643","status":"public","keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2023-08-02T13:53:11Z","file_date_updated":"2022-01-19T09:27:43Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"acknowledgement":"J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged.","publisher":"Cambridge University Press","quality_controlled":"1","oa":1,"day":"18","publication":"Forum of Mathematics, Sigma","has_accepted_license":"1","isi":1,"year":"2022","date_published":"2022-01-18T00:00:00Z","doi":"10.1017/fms.2021.80","date_created":"2022-01-18T16:18:51Z","article_number":"e4","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. 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The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 2022;25(1). doi:10.1007/s11040-021-09415-0","apa":"Henheik, S. J. (2022). The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. Springer Nature. https://doi.org/10.1007/s11040-021-09415-0","short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).","ieee":"S. J. Henheik, “The BCS critical temperature at high density,” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1. Springer Nature, 2022.","mla":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1, 3, Springer Nature, 2022, doi:10.1007/s11040-021-09415-0.","ista":"Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3.","chicago":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” Mathematical Physics, Analysis and Geometry. Springer Nature, 2022. https://doi.org/10.1007/s11040-021-09415-0."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"}],"external_id":{"arxiv":["2106.02015"],"isi":["000741387600001"]},"article_processing_charge":"Yes (via OA deal)","title":"The BCS critical temperature at high density","acknowledgement":"I am very grateful to Robert Seiringer for his guidance during this project and for many valuable comments on an earlier version of the manuscript. Moreover, I would like to thank Asbjørn Bækgaard Lauritsen for many helpful discussions and comments, pointing out the reference [22] and for his involvement in a closely related joint project [13]. Finally, I am grateful to Christian Hainzl for valuable comments on an earlier version of the manuscript and Andreas Deuchert for interesting discussions.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"isi":1,"has_accepted_license":"1","year":"2022","day":"11","publication":"Mathematical Physics, Analysis and Geometry","doi":"10.1007/s11040-021-09415-0","date_published":"2022-01-11T00:00:00Z","date_created":"2022-01-13T15:40:53Z","_id":"10623","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["geometry and topology","mathematical physics"],"date_updated":"2023-08-02T13:51:52Z","ddc":["514"],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-14T07:27:45Z","abstract":[{"text":"We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"01","intvolume":" 25","publication_identifier":{"issn":["1385-0172"],"eissn":["1572-9656"]},"publication_status":"published","file":[{"date_created":"2022-01-14T07:27:45Z","file_name":"2022_MathPhyAnalGeo_Henheik.pdf","creator":"cchlebak","date_updated":"2022-01-14T07:27:45Z","file_size":505804,"file_id":"10624","checksum":"d44f8123a52592a75b2c3b8ee2cd2435","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"issue":"1","volume":25,"ec_funded":1},{"_id":"10732","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","date_updated":"2023-08-02T14:12:35Z","ddc":["500"],"department":[{"_id":"LaEr"}],"file_date_updated":"2022-07-29T07:22:08Z","abstract":[{"text":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to eitW for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"04","intvolume":" 282","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"publication_status":"published","file":[{"date_created":"2022-07-29T07:22:08Z","file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","date_updated":"2022-07-29T07:22:08Z","file_size":652573,"creator":"dernst","checksum":"b75fdad606ab507dc61109e0907d86c0","file_id":"11690","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"volume":282,"issue":"8","article_number":"109394","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation for Wigner Matrices.” Journal of Functional Analysis. Elsevier, 2022. https://doi.org/10.1016/j.jfa.2022.109394.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Thermalisation for Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109394","ama":"Cipolloni G, Erdös L, Schröder DJ. Thermalisation for Wigner matrices. Journal of Functional Analysis. 2022;282(8). doi:10.1016/j.jfa.2022.109394","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” Journal of Functional Analysis, vol. 282, no. 8. Elsevier, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022).","mla":"Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” Journal of Functional Analysis, vol. 282, no. 8, 109394, Elsevier, 2022, doi:10.1016/j.jfa.2022.109394."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000781239100004"],"arxiv":["2102.09975"]},"title":"Thermalisation for Wigner matrices","acknowledgement":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.","quality_controlled":"1","publisher":"Elsevier","oa":1,"has_accepted_license":"1","isi":1,"year":"2022","day":"15","publication":"Journal of Functional Analysis","date_published":"2022-04-15T00:00:00Z","doi":"10.1016/j.jfa.2022.109394","date_created":"2022-02-06T23:01:30Z"},{"volume":11,"issue":"4","language":[{"iso":"eng"}],"publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"publication_status":"published","month":"10","intvolume":" 11","scopus_import":"1","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2103.03906","open_access":"1"}],"oa_version":"Preprint","abstract":[{"text":"We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one.","lang":"eng"}],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_updated":"2023-08-03T06:32:22Z","status":"public","keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"article_type":"original","type":"journal_article","_id":"11135","doi":"10.1142/s2010326322500368","date_published":"2022-10-01T00:00:00Z","date_created":"2022-04-08T07:11:12Z","day":"01","publication":"Random Matrices: Theory and Applications","isi":1,"year":"2022","publisher":"World Scientific","quality_controlled":"1","oa":1,"title":"On the operator norm of a Hermitian random matrix with correlated entries","author":[{"last_name":"Reker","full_name":"Reker, Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana"}],"external_id":{"isi":["000848873800001"],"arxiv":["2103.03906"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” Random Matrices: Theory and Applications. World Scientific, 2022. https://doi.org/10.1142/s2010326322500368.","ista":"Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.","mla":"Reker, Jana. “On the Operator Norm of a Hermitian Random Matrix with Correlated Entries.” Random Matrices: Theory and Applications, vol. 11, no. 4, 2250036, World Scientific, 2022, doi:10.1142/s2010326322500368.","short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","ieee":"J. Reker, “On the operator norm of a Hermitian random matrix with correlated entries,” Random Matrices: Theory and Applications, vol. 11, no. 4. World Scientific, 2022.","apa":"Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. World Scientific. https://doi.org/10.1142/s2010326322500368","ama":"Reker J. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 2022;11(4). doi:10.1142/s2010326322500368"},"article_number":"2250036"},{"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","_id":"11332","department":[{"_id":"LaEr"}],"file_date_updated":"2022-08-05T06:01:13Z","ddc":["510"],"date_updated":"2023-08-03T06:34:24Z","intvolume":" 393","month":"07","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size N converge to the Tracy–Widom laws at a rate O(N^{-1/3+\\omega }), as N tends to infinity. For Wigner matrices this improves the previous rate O(N^{-2/9+\\omega }) obtained by Bourgade (J Eur Math Soc, 2021) for generalized Wigner matrices. Our result follows from a Green function comparison theorem, originally introduced by Erdős et al. (Adv Math 229(3):1435–1515, 2012) to prove edge universality, on a finer spectral parameter scale with improved error estimates. The proof relies on the continuous Green function flow induced by a matrix-valued Ornstein–Uhlenbeck process. Precise estimates on leading contributions from the third and fourth order moments of the matrix entries are obtained using iterative cumulant expansions and recursive comparisons for correlation functions, along with uniform convergence estimates for correlation kernels of the Gaussian invariant ensembles."}],"ec_funded":1,"volume":393,"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","file_id":"11726","success":1,"creator":"dernst","date_updated":"2022-08-05T06:01:13Z","file_size":1141462,"date_created":"2022-08-05T06:01:13Z","file_name":"2022_CommunMathPhys_Schnelli.pdf"}],"publication_status":"published","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","article_processing_charge":"No","external_id":{"arxiv":["2102.04330"],"isi":["000782737200001"]},"author":[{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","last_name":"Schnelli"},{"last_name":"Xu","full_name":"Xu, Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s00220-022-04377-y.","ista":"Schnelli K, Xu Y. 2022. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 393, 839–907.","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical Physics, vol. 393, Springer Nature, 2022, pp. 839–907, doi:10.1007/s00220-022-04377-y.","apa":"Schnelli, K., & Xu, Y. (2022). Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-022-04377-y","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 2022;393:839-907. doi:10.1007/s00220-022-04377-y","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907.","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices,” Communications in Mathematical Physics, vol. 393. Springer Nature, pp. 839–907, 2022."},"oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"Kevin Schnelli is supported in parts by the Swedish Research Council Grant VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Yuanyuan Xu is supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","date_created":"2022-04-24T22:01:44Z","date_published":"2022-07-01T00:00:00Z","doi":"10.1007/s00220-022-04377-y","page":"839-907","publication":"Communications in Mathematical Physics","day":"01","year":"2022","has_accepted_license":"1","isi":1},{"issue":"3","volume":50,"publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"month":"05","intvolume":" 50","abstract":[{"text":"We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048).","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"LaEr"}],"date_updated":"2023-08-03T07:16:53Z","type":"journal_article","article_type":"original","status":"public","_id":"11418","page":"984-1012","doi":"10.1214/21-AOP1552","date_published":"2022-05-01T00:00:00Z","date_created":"2022-05-29T22:01:53Z","isi":1,"year":"2022","day":"01","publication":"Annals of Probability","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"acknowledgement":"L.E. would like to thank Zhigang Bao for many illuminating discussions in an early stage of this research. The authors are also grateful to Paul Bourgade for his comments on the manuscript and the anonymous referee for several useful suggestions.","author":[{"orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"arxiv":["2103.06730"],"isi":["000793963400005"]},"article_processing_charge":"No","title":"Normal fluctuation in quantum ergodicity for Wigner matrices","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 2022;50(3):984-1012. doi:10.1214/21-AOP1552","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-AOP1552","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 984–1012.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” Annals of Probability, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022.","mla":"Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” Annals of Probability, vol. 50, no. 3, Institute of Mathematical Statistics, 2022, pp. 984–1012, doi:10.1214/21-AOP1552.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” Annals of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1552."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"abstract":[{"lang":"eng","text":"A recently proposed approach for avoiding the ultraviolet divergence of Hamiltonians with particle creation is based on interior-boundary conditions (IBCs). The approach works well in the non-relativistic case, i.e., for the Laplacian operator. Here, we study how the approach can be applied to Dirac operators. While this has successfully been done already in one space dimension, and more generally for codimension-1 boundaries, the situation of point sources in three dimensions corresponds to a codimension-3 boundary. One would expect that, for such a boundary, Dirac operators do not allow for boundary conditions because they are known not to allow for point interactions in 3D, which also correspond to a boundary condition. Indeed, we confirm this expectation here by proving that there is no self-adjoint operator on a (truncated) Fock space that would correspond to a Dirac operator with an IBC at configurations with a particle at the origin. However, we also present a positive result showing that there are self-adjoint operators with an IBC (on the boundary consisting of configurations with a particle at the origin) that are away from those configurations, given by a Dirac operator plus a sufficiently strong Coulomb potential."}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 63","month":"12","publication_status":"published","publication_identifier":{"issn":["0022-2488"]},"language":[{"iso":"eng"}],"file":[{"date_created":"2023-01-20T11:58:59Z","file_name":"2022_JourMathPhysics_Henheik.pdf","date_updated":"2023-01-20T11:58:59Z","file_size":5436804,"creator":"dernst","file_id":"12327","checksum":"5150287295e0ce4f12462c990744d65d","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"ec_funded":1,"volume":63,"issue":"12","_id":"12110","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","date_updated":"2023-08-03T14:12:01Z","ddc":["510"],"file_date_updated":"2023-01-20T11:58:59Z","department":[{"_id":"LaEr"}],"acknowledgement":"J.H. gratefully acknowledges the partial financial support by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n","oa":1,"quality_controlled":"1","publisher":"AIP Publishing","year":"2022","has_accepted_license":"1","isi":1,"publication":"Journal of Mathematical Physics","day":"01","date_created":"2023-01-08T23:00:53Z","doi":"10.1063/5.0104675","date_published":"2022-12-01T00:00:00Z","article_number":"122302","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"citation":{"chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104675.","ista":"Henheik SJ, Tumulka R. 2022. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 63(12), 122302.","mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical Physics, vol. 63, no. 12, 122302, AIP Publishing, 2022, doi:10.1063/5.0104675.","short":"S.J. Henheik, R. Tumulka, Journal of Mathematical Physics 63 (2022).","ieee":"S. J. Henheik and R. Tumulka, “Interior-boundary conditions for the Dirac equation at point sources in three dimensions,” Journal of Mathematical Physics, vol. 63, no. 12. AIP Publishing, 2022.","ama":"Henheik SJ, Tumulka R. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 2022;63(12). doi:10.1063/5.0104675","apa":"Henheik, S. J., & Tumulka, R. (2022). Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0104675"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000900748900002"]},"article_processing_charge":"No","author":[{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"first_name":"Roderich","full_name":"Tumulka, Roderich","last_name":"Tumulka"}],"title":"Interior-boundary conditions for the Dirac equation at point sources in three dimensions"},{"department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-24T10:02:40Z","date_updated":"2023-08-04T09:00:35Z","ddc":["510"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"_id":"12148","volume":10,"ec_funded":1,"publication_identifier":{"issn":["2050-5094"]},"publication_status":"published","file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"12356","checksum":"94a049aeb1eea5497aa097712a73c400","success":1,"date_updated":"2023-01-24T10:02:40Z","file_size":817089,"creator":"dernst","date_created":"2023-01-24T10:02:40Z","file_name":"2022_ForumMath_Cipolloni.pdf"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"10","intvolume":" 10","abstract":[{"text":"We prove a general local law for Wigner matrices that optimally handles observables of arbitrary rank and thus unifies the well-known averaged and isotropic local laws. As an application, we prove a central limit theorem in quantum unique ergodicity (QUE): that is, we show that the quadratic forms of a general deterministic matrix A on the bulk eigenvectors of a Wigner matrix have approximately Gaussian fluctuation. For the bulk spectrum, we thus generalise our previous result [17] as valid for test matrices A of large rank as well as the result of Benigni and Lopatto [7] as valid for specific small-rank observables.","lang":"eng"}],"oa_version":"Published Version","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"article_processing_charge":"No","external_id":{"isi":["000873719200001"]},"title":"Rank-uniform local law for Wigner matrices","citation":{"mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 10, e96, Cambridge University Press, 2022, doi:10.1017/fms.2022.86.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2022.86","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2022.86","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2022.86.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 10, e96."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"article_number":"e96","date_published":"2022-10-27T00:00:00Z","doi":"10.1017/fms.2022.86","date_created":"2023-01-12T12:07:30Z","has_accepted_license":"1","isi":1,"year":"2022","day":"27","publication":"Forum of Mathematics, Sigma","quality_controlled":"1","publisher":"Cambridge University Press","oa":1,"acknowledgement":"L.E. acknowledges support by ERC Advanced Grant ‘RMTBeyond’ No. 101020331. D.S. acknowledges the support of Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation."},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Henheik SJ, Wessel T. 2022. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 63(12), 121101.","chicago":"Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0123441.","apa":"Henheik, S. J., & Wessel, T. (2022). On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0123441","ama":"Henheik SJ, Wessel T. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 2022;63(12). doi:10.1063/5.0123441","ieee":"S. J. Henheik and T. Wessel, “On adiabatic theory for extended fermionic lattice systems,” Journal of Mathematical Physics, vol. 63, no. 12. AIP Publishing, 2022.","short":"S.J. Henheik, T. Wessel, Journal of Mathematical Physics 63 (2022).","mla":"Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” Journal of Mathematical Physics, vol. 63, no. 12, 121101, AIP Publishing, 2022, doi:10.1063/5.0123441."},"title":"On adiabatic theory for extended fermionic lattice systems","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X"},{"last_name":"Wessel","full_name":"Wessel, Tom","first_name":"Tom"}],"article_processing_charge":"No","external_id":{"arxiv":["2208.12220"],"isi":["000905776200001"]},"article_number":"121101","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"day":"01","publication":"Journal of Mathematical Physics","has_accepted_license":"1","isi":1,"year":"2022","doi":"10.1063/5.0123441","date_published":"2022-12-01T00:00:00Z","date_created":"2023-01-15T23:00:52Z","acknowledgement":"It is a pleasure to thank Stefan Teufel for numerous interesting discussions, fruitful collaboration, and many helpful comments on an earlier version of the manuscript. J.H. acknowledges partial financial support from the ERC Advanced Grant No. 101020331 “Random\r\nmatrices beyond Wigner-Dyson-Mehta.” T.W. acknowledges financial support from the DFG research unit FOR 5413 “Long-range interacting quantum spin systems out of equilibrium: Experiment, Theory and Mathematics.\" ","publisher":"AIP Publishing","quality_controlled":"1","oa":1,"ddc":["510"],"date_updated":"2023-08-04T09:14:57Z","file_date_updated":"2023-01-27T07:10:52Z","department":[{"_id":"LaEr"}],"_id":"12184","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"12410","checksum":"213b93750080460718c050e4967cfdb4","creator":"dernst","file_size":5251092,"date_updated":"2023-01-27T07:10:52Z","file_name":"2022_JourMathPhysics_Henheik2.pdf","date_created":"2023-01-27T07:10:52Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-2488"]},"publication_status":"published","volume":63,"issue":"12","ec_funded":1,"oa_version":"Published Version","abstract":[{"text":"We review recent results on adiabatic theory for ground states of extended gapped fermionic lattice systems under several different assumptions. More precisely, we present generalized super-adiabatic theorems for extended but finite and infinite systems, assuming either a uniform gap or a gap in the bulk above the unperturbed ground state. The goal of this Review is to provide an overview of these adiabatic theorems and briefly outline the main ideas and techniques required in their proofs.","lang":"eng"}],"month":"12","intvolume":" 63","scopus_import":"1"},{"article_type":"original","type":"journal_article","keyword":["General Mathematics"],"status":"public","_id":"12214","department":[{"_id":"LaEr"}],"date_updated":"2023-08-04T09:24:17Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2102.02037"}],"scopus_import":"1","intvolume":" 106","month":"09","abstract":[{"text":"Motivated by Kloeckner’s result on the isometry group of the quadratic Wasserstein space W2(Rn), we describe the isometry group Isom(Wp(E)) for all parameters 0 < p < ∞ and for all separable real Hilbert spaces E. In particular, we show that Wp(X) is isometrically rigid for all Polish space X whenever 0 < p < 1. This is a consequence of our more general result: we prove that W1(X) is isometrically rigid if X is a complete separable metric space that satisfies the strict triangle inequality. Furthermore, we show that this latter rigidity result does not generalise to parameters p > 1, by solving Kloeckner’s problem affirmatively on the existence of mass-splitting isometries. ","lang":"eng"}],"oa_version":"Preprint","ec_funded":1,"volume":106,"issue":"4","publication_status":"published","publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425","name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294"}],"article_processing_charge":"No","external_id":{"isi":["000854878500001"],"arxiv":["2102.02037"]},"author":[{"first_name":"György Pál","last_name":"Gehér","full_name":"Gehér, György Pál"},{"first_name":"Tamás","last_name":"Titkos","full_name":"Titkos, Tamás"},{"last_name":"Virosztek","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"title":"The isometry group of Wasserstein spaces: The Hilbertian case","citation":{"chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical Society. Wiley, 2022. https://doi.org/10.1112/jlms.12676.","ista":"Gehér GP, Titkos T, Virosztek D. 2022. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 106(4), 3865–3894.","mla":"Gehér, György Pál, et al. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical Society, vol. 106, no. 4, Wiley, 2022, pp. 3865–94, doi:10.1112/jlms.12676.","apa":"Gehér, G. P., Titkos, T., & Virosztek, D. (2022). The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12676","ama":"Gehér GP, Titkos T, Virosztek D. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 2022;106(4):3865-3894. doi:10.1112/jlms.12676","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society 106 (2022) 3865–3894.","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “The isometry group of Wasserstein spaces: The Hilbertian case,” Journal of the London Mathematical Society, vol. 106, no. 4. Wiley, pp. 3865–3894, 2022."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"publisher":"Wiley","quality_controlled":"1","acknowledgement":"Geher was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125), and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383 and K134944).\r\nTitkos was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374, grant no. K115383 and K134944), by the J´anos Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the UNKP-20-5-BGE-1 New National Excellence Program of the ´Ministry of Innovation and Technology.\r\nVirosztek was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, by the Momentum program of the Hungarian Academy of Sciences under grant agreement no. LP2021-15/2021, and partially supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grants no. K124152 and no. KH129601). ","page":"3865-3894","date_created":"2023-01-16T09:46:13Z","doi":"10.1112/jlms.12676","date_published":"2022-09-18T00:00:00Z","year":"2022","isi":1,"publication":"Journal of the London Mathematical Society","day":"18"},{"has_accepted_license":"1","isi":1,"year":"2022","day":"01","publication":"Annales Henri Poincaré","page":"3981-4002","date_published":"2022-11-01T00:00:00Z","doi":"10.1007/s00023-022-01188-8","date_created":"2023-01-16T09:50:26Z","acknowledgement":"Open access funding provided by Swiss Federal Institute of Technology Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"citation":{"mla":"Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:10.1007/s00023-022-01188-8.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” Annales Henri Poincaré, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. Springer Nature. https://doi.org/10.1007/s00023-022-01188-8","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 2022;23(11):3981-4002. doi:10.1007/s00023-022-01188-8","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré. Springer Nature, 2022. https://doi.org/10.1007/s00023-022-01188-8.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"external_id":{"isi":["000796323500001"]},"article_processing_charge":"No","title":"Density of small singular values of the shifted real Ginibre ensemble","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"publication_status":"published","file":[{"success":1,"file_id":"12424","checksum":"5582f059feeb2f63e2eb68197a34d7dc","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","date_created":"2023-01-27T11:06:47Z","creator":"dernst","file_size":1333638,"date_updated":"2023-01-27T11:06:47Z"}],"language":[{"iso":"eng"}],"volume":23,"issue":"11","abstract":[{"text":"We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"11","intvolume":" 23","date_updated":"2023-08-04T09:33:52Z","ddc":["510"],"department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-27T11:06:47Z","_id":"12232","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"]},{"date_published":"2022-10-14T00:00:00Z","doi":"10.1063/5.0104290","date_created":"2023-01-16T09:52:58Z","isi":1,"has_accepted_license":"1","year":"2022","day":"14","publication":"Journal of Mathematical Physics","quality_controlled":"1","publisher":"AIP Publishing","oa":1,"acknowledgement":"The authors are grateful to G. Akemann for bringing Refs. 19 and 24–26 to their attention. Discussions with Guillaume Dubach on a preliminary version of this project are acknowledged.\r\nL.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331. D.S. was supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan","last_name":"Xu","full_name":"Xu, Yuanyuan"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000869715800001"],"arxiv":["2206.04443"]},"title":"Directional extremal statistics for Ginibre eigenvalues","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 2022;63(10). doi:10.1063/5.0104290","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2022). Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0104290","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” Journal of Mathematical Physics, vol. 63, no. 10. AIP Publishing, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022).","mla":"Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical Physics, vol. 63, no. 10, 103303, AIP Publishing, 2022, doi:10.1063/5.0104290.","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104290."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"article_number":"103303","volume":63,"issue":"10","ec_funded":1,"publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"12436","checksum":"2db278ae5b07f345a7e3fec1f92b5c33","file_size":7356807,"date_updated":"2023-01-30T08:01:10Z","creator":"dernst","file_name":"2022_JourMathPhysics_Cipolloni2.pdf","date_created":"2023-01-30T08:01:10Z"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"10","intvolume":" 63","abstract":[{"lang":"eng","text":"We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. "}],"oa_version":"Published Version","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-30T08:01:10Z","date_updated":"2023-08-04T09:40:02Z","ddc":["510","530"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"_id":"12243"},{"publication_identifier":{"eissn":["1083-6489"]},"publication_status":"published","file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"12464","checksum":"bb647b48fbdb59361210e425c220cdcb","success":1,"date_updated":"2023-01-30T11:59:21Z","file_size":502149,"creator":"dernst","date_created":"2023-01-30T11:59:21Z","file_name":"2022_ElecJournProbability_Cipolloni.pdf"}],"language":[{"iso":"eng"}],"volume":27,"ec_funded":1,"abstract":[{"lang":"eng","text":"We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale."}],"oa_version":"Published Version","scopus_import":"1","month":"09","intvolume":" 27","date_updated":"2023-08-04T10:32:23Z","ddc":["510"],"file_date_updated":"2023-01-30T11:59:21Z","department":[{"_id":"LaEr"}],"_id":"12290","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"has_accepted_license":"1","isi":1,"year":"2022","day":"12","publication":"Electronic Journal of Probability","page":"1-38","date_published":"2022-09-12T00:00:00Z","doi":"10.1214/22-ejp838","date_created":"2023-01-16T10:04:38Z","acknowledgement":"L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331. D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"citation":{"mla":"Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” Electronic Journal of Probability, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:10.1214/22-ejp838.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” Electronic Journal of Probability, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 2022;27:1-38. doi:10.1214/22-ejp838","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-ejp838","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/22-ejp838.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"article_processing_charge":"No","external_id":{"isi":["000910863700003"]},"title":"Optimal multi-resolvent local laws for Wigner matrices","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}]},{"acknowledgement":"We are grateful to Robert Seiringer for helpful discussions and many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open access funding provided by Institute of Science and Technology (IST Austria)","publisher":"Springer Nature","quality_controlled":"1","oa":1,"day":"29","publication":"Journal of Statistical Physics","has_accepted_license":"1","isi":1,"year":"2022","doi":"10.1007/s10955-022-02965-9","date_published":"2022-07-29T00:00:00Z","date_created":"2022-08-05T11:36:56Z","article_number":"5","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).","ieee":"S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal of Statistical Physics, vol. 189. Springer Nature, 2022.","ama":"Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9","apa":"Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9","mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature, 2022, doi:10.1007/s10955-022-02965-9.","ista":"Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5.","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02965-9."},"title":"The BCS energy gap at high density","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","last_name":"Lauritsen","orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000833007200002"]},"oa_version":"Published Version","abstract":[{"lang":"eng","text":"We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature."}],"month":"07","intvolume":" 189","scopus_import":"1","file":[{"success":1,"checksum":"b398c4dbf65f71d417981d6e366427e9","file_id":"11746","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2022_JourStatisticalPhysics_Henheik.pdf","date_created":"2022-08-08T07:36:34Z","file_size":419563,"date_updated":"2022-08-08T07:36:34Z","creator":"dernst"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"publication_status":"published","volume":189,"ec_funded":1,"_id":"11732","status":"public","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["530"],"date_updated":"2023-09-05T14:57:49Z","file_date_updated":"2022-08-08T07:36:34Z","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}]},{"date_created":"2021-11-14T23:01:25Z","date_published":"2021-09-28T00:00:00Z","doi":"10.1214/21-EJP686","publication":"Electronic Journal of Probability","day":"28","year":"2021","has_accepted_license":"1","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","acknowledgement":"We acknowledge partial support from the grants NSF DMS-1812114 of P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI). This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We would like to thank Paul Bourgade and László Erdős for many helpful comments.","title":"On eigenvector statistics in the spherical and truncated unitary ensembles","article_processing_charge":"No","author":[{"full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"short":"G. Dubach, Electronic Journal of Probability 26 (2021).","ieee":"G. Dubach, “On eigenvector statistics in the spherical and truncated unitary ensembles,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021.","ama":"Dubach G. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP686","apa":"Dubach, G. (2021). On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP686","mla":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” Electronic Journal of Probability, vol. 26, 124, Institute of Mathematical Statistics, 2021, doi:10.1214/21-EJP686.","ista":"Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 26, 124.","chicago":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP686."},"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"article_number":"124","ec_funded":1,"volume":26,"language":[{"iso":"eng"}],"file":[{"date_created":"2021-11-15T10:10:17Z","file_name":"2021_ElecJournalProb_Dubach.pdf","creator":"cchlebak","date_updated":"2021-11-15T10:10:17Z","file_size":735940,"file_id":"10288","checksum":"1c975afb31460277ce4d22b93538e5f9","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"eissn":["1083-6489"]},"intvolume":" 26","month":"09","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We study the overlaps between right and left eigenvectors for random matrices of the spherical ensemble, as well as truncated unitary ensembles in the regime where half of the matrix at least is truncated. These two integrable models exhibit a form of duality, and the essential steps of our investigation can therefore be performed in parallel. In every case, conditionally on all eigenvalues, diagonal overlaps are shown to be distributed as a product of independent random variables with explicit distributions. This enables us to prove that the scaled diagonal overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail limit, namely, the inverse of a γ2 distribution. We also provide formulae for the conditional expectation of diagonal and off-diagonal overlaps, either with respect to one eigenvalue, or with respect to the whole spectrum. These results, analogous to what is known for the complex Ginibre ensemble, can be obtained in these cases thanks to integration techniques inspired from a previous work by Forrester & Krishnapur."}],"department":[{"_id":"LaEr"}],"file_date_updated":"2021-11-15T10:10:17Z","ddc":["519"],"date_updated":"2021-11-15T10:48:46Z","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","_id":"10285"},{"citation":{"short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).","ieee":"L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the Riemann zeta function over intervals of varying length,” arXiv. .","apa":"Arguin, L.-P., Dubach, G., & Hartung, L. (n.d.). Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv. https://doi.org/10.48550/arXiv.2103.04817","ama":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv. doi:10.48550/arXiv.2103.04817","mla":"Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv, 2103.04817, doi:10.48550/arXiv.2103.04817.","ista":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv, 2103.04817.","chicago":"Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.04817."},"date_updated":"2023-05-03T10:22:59Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Louis-Pierre","full_name":"Arguin, Louis-Pierre","last_name":"Arguin"},{"first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach","full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137"},{"first_name":"Lisa","last_name":"Hartung","full_name":"Hartung, Lisa"}],"article_processing_charge":"No","external_id":{"arxiv":["2103.04817"]},"title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","department":[{"_id":"LaEr"}],"_id":"9230","article_number":"2103.04817","type":"preprint","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"status":"public","publication_status":"submitted","year":"2021","day":"08","language":[{"iso":"eng"}],"publication":"arXiv","date_published":"2021-03-08T00:00:00Z","doi":"10.48550/arXiv.2103.04817","date_created":"2021-03-09T11:08:15Z","ec_funded":1,"abstract":[{"lang":"eng","text":"We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length (log T)θ, where θ is either fixed or tends to zero at a suitable rate.\r\nIt is shown that the deterministic level of the maximum interpolates smoothly between the ones\r\nof log-correlated variables and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to 1/4’ in the second order. This provides a natural context where extreme value statistics of\r\nlog-correlated variables with time-dependent variance and rate occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian correction. This correction is expected to be present for the\r\nRiemann zeta function and pertains to the question of the correct order of the maximum of\r\nthe zeta function in large intervals."}],"oa_version":"Preprint","acknowledgement":"The research of L.-P. A. is supported in part by the grant NSF CAREER DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID 443891315 within SPP 2265 and Project-ID 446173099.","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.04817"}],"month":"03"},{"external_id":{"arxiv":["2103.11389"]},"article_processing_charge":"No","author":[{"last_name":"Dubach","full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume"},{"orcid":"0000-0003-1548-0177","full_name":"Mühlböck, Fabian","last_name":"Mühlböck","id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425","first_name":"Fabian"}],"title":"Formal verification of Zagier's one-sentence proof","department":[{"_id":"LaEr"},{"_id":"ToHe"}],"citation":{"ieee":"G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,” arXiv. .","short":"G. Dubach, F. Mühlböck, ArXiv (n.d.).","apa":"Dubach, G., & Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence proof. arXiv. https://doi.org/10.48550/arXiv.2103.11389","ama":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv. doi:10.48550/arXiv.2103.11389","mla":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” ArXiv, 2103.11389, doi:10.48550/arXiv.2103.11389.","ista":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv, 2103.11389.","chicago":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.11389."},"date_updated":"2023-05-03T10:26:45Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"preprint","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"status":"public","_id":"9281","article_number":"2103.11389","date_created":"2021-03-23T05:38:48Z","ec_funded":1,"doi":"10.48550/arXiv.2103.11389","related_material":{"record":[{"relation":"other","status":"public","id":"9946"}]},"date_published":"2021-03-21T00:00:00Z","year":"2021","publication_status":"submitted","publication":"arXiv","language":[{"iso":"eng"}],"day":"21","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.11389"}],"oa":1,"month":"03","abstract":[{"lang":"eng","text":"We comment on two formal proofs of Fermat's sum of two squares theorem, written using the Mathematical Components libraries of the Coq proof assistant. The first one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's recent new proof relying on partition-theoretic arguments. Both formal proofs rely on a general property of involutions of finite sets, of independent interest. The proof technique consists for the most part of automating recurrent tasks (such as case distinctions and computations on natural numbers) via ad hoc tactics."}],"oa_version":"Preprint"},{"main_file_link":[{"url":"https://arxiv.org/abs/2002.11678","open_access":"1"}],"intvolume":" 609","month":"01","abstract":[{"text":"It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted A#H-mean introduced by Kim, Lawson, and Lim.","lang":"eng"}],"oa_version":"Preprint","ec_funded":1,"volume":609,"publication_status":"published","publication_identifier":{"issn":["0024-3795"]},"language":[{"iso":"eng"}],"type":"journal_article","article_type":"original","keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"status":"public","_id":"8373","department":[{"_id":"LaEr"}],"date_updated":"2023-08-04T10:58:14Z","oa":1,"quality_controlled":"1","publisher":"Elsevier","acknowledgement":"The authors are grateful to Milán Mosonyi for fruitful discussions on the topic, and to the anonymous referee for his/her comments and suggestions.\r\nJ. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant for Quantum Information Theory, No. 96 141, and by Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K119442, no. K124152, and no. KH129601. D. Virosztek was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01), by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","page":"203-217","date_created":"2020-09-11T08:35:50Z","date_published":"2021-01-15T00:00:00Z","doi":"10.1016/j.laa.2020.09.007","year":"2021","isi":1,"publication":"Linear Algebra and its Applications","day":"15","project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425"},{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_processing_charge":"No","external_id":{"isi":["000581730500011"],"arxiv":["2002.11678"]},"author":[{"first_name":"József","last_name":"Pitrik","full_name":"Pitrik, József"},{"last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel"}],"title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","citation":{"ista":"Pitrik J, Virosztek D. 2021. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 609, 203–217.","chicago":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” Linear Algebra and Its Applications. Elsevier, 2021. https://doi.org/10.1016/j.laa.2020.09.007.","short":"J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.","ieee":"J. Pitrik and D. Virosztek, “A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means,” Linear Algebra and its Applications, vol. 609. Elsevier, pp. 203–217, 2021.","ama":"Pitrik J, Virosztek D. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 2021;609:203-217. doi:10.1016/j.laa.2020.09.007","apa":"Pitrik, J., & Virosztek, D. (2021). A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2020.09.007","mla":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” Linear Algebra and Its Applications, vol. 609, Elsevier, 2021, pp. 203–17, doi:10.1016/j.laa.2020.09.007."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"title":"The metric property of the quantum Jensen-Shannon divergence","author":[{"last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel"}],"external_id":{"arxiv":["1910.10447"],"isi":["000619676100035"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"apa":"Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107595","ama":"Virosztek D. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 2021;380(3). doi:10.1016/j.aim.2021.107595","ieee":"D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” Advances in Mathematics, vol. 380, no. 3. Elsevier, 2021.","short":"D. Virosztek, Advances in Mathematics 380 (2021).","mla":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics, vol. 380, no. 3, 107595, Elsevier, 2021, doi:10.1016/j.aim.2021.107595.","ista":"Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 380(3), 107595.","chicago":"Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107595."},"project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"article_number":"107595","date_published":"2021-03-26T00:00:00Z","doi":"10.1016/j.aim.2021.107595","date_created":"2021-01-22T17:55:17Z","day":"26","publication":"Advances in Mathematics","isi":1,"year":"2021","publisher":"Elsevier","quality_controlled":"1","oa":1,"acknowledgement":"D. Virosztek was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","department":[{"_id":"LaEr"}],"date_updated":"2023-08-07T13:34:48Z","status":"public","keyword":["General Mathematics"],"type":"journal_article","article_type":"original","_id":"9036","issue":"3","volume":380,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0001-8708"]},"publication_status":"published","month":"03","intvolume":" 380","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.10447"}],"oa_version":"Preprint","abstract":[{"text":"In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space.","lang":"eng"}]},{"external_id":{"arxiv":["2002.02438"],"isi":["000641855600001"]},"article_processing_charge":"No","author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"title":"Fluctuation around the circular law for random matrices with real entries","citation":{"mla":"Cipolloni, Giorgio, et al. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” Electronic Journal of Probability, vol. 26, 24, Institute of Mathematical Statistics, 2021, doi:10.1214/21-EJP591.","ama":"Cipolloni G, Erdös L, Schröder DJ. Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP591","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP591","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 26 (2021).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular law for random matrices with real entries,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP591.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. 26, 24."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"article_number":"24","date_created":"2021-05-23T22:01:44Z","doi":"10.1214/21-EJP591","date_published":"2021-03-23T00:00:00Z","year":"2021","has_accepted_license":"1","isi":1,"publication":"Electronic Journal of Probability","day":"23","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"file_date_updated":"2021-05-25T13:24:19Z","date_updated":"2023-08-08T13:39:19Z","ddc":["510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","status":"public","_id":"9412","ec_funded":1,"volume":26,"publication_status":"published","publication_identifier":{"eissn":["10836489"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"864ab003ad4cffea783f65aa8c2ba69f","file_id":"9423","success":1,"date_updated":"2021-05-25T13:24:19Z","file_size":865148,"creator":"kschuh","date_created":"2021-05-25T13:24:19Z","file_name":"2021_EJP_Cipolloni.pdf"}],"scopus_import":"1","intvolume":" 26","month":"03","abstract":[{"lang":"eng","text":"We extend our recent result [22] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices X with independent, identically distributed complex entries to the real symmetry class. We find that the expectation and variance substantially differ from their complex counterparts, reflecting (i) the special spectral symmetry of real matrices onto the real axis; and (ii) the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes the previously known special cases where either the test function is analytic [49] or the first four moments of the matrix elements match the real Gaussian [59, 44]. The key element of the proof is the analysis of several weakly dependent Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared with [22] is that the correlation structure of the stochastic differentials in each individual DBM is non-trivial, potentially even jeopardising its well-posedness."}],"oa_version":"Published Version"},{"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"article_number":"e44","title":"Equipartition principle for Wigner matrices","author":[{"last_name":"Bao","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"}],"external_id":{"isi":["000654960800001"],"arxiv":["2008.07061"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2021. https://doi.org/10.1017/fms.2021.38.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2021). Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.38","ama":"Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.38","short":"Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021.","mla":"Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 9, e44, Cambridge University Press, 2021, doi:10.1017/fms.2021.38."},"quality_controlled":"1","publisher":"Cambridge University Press","oa":1,"acknowledgement":"The first author is supported in part by Hong Kong RGC Grant GRF 16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced Grant RANMAT 338804. The third author is supported in part by Swedish Research Council Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation","date_published":"2021-05-27T00:00:00Z","doi":"10.1017/fms.2021.38","date_created":"2021-06-13T22:01:33Z","day":"27","publication":"Forum of Mathematics, Sigma","isi":1,"has_accepted_license":"1","year":"2021","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"9550","file_date_updated":"2021-06-15T14:40:45Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2023-08-08T14:03:40Z","month":"05","intvolume":" 9","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices. "}],"volume":9,"ec_funded":1,"file":[{"date_updated":"2021-06-15T14:40:45Z","file_size":483458,"creator":"cziletti","date_created":"2021-06-15T14:40:45Z","file_name":"2021_ForumMath_Bao.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"9555","checksum":"47c986578de132200d41e6d391905519","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["20505094"]},"publication_status":"published"},{"_id":"9912","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2023-08-11T10:31:48Z","department":[{"_id":"LaEr"}],"file_date_updated":"2022-05-12T12:50:27Z","oa_version":"Published Version","abstract":[{"lang":"eng","text":"In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via 𝑁≪𝑀 channels, the density 𝜌 of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio 𝜙:=𝑁/𝑀≤1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit 𝜙→0, we recover the formula for the density 𝜌 that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any 𝜙<1 but in the borderline case 𝜙=1 an anomalous 𝜆−2/3 singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries."}],"month":"12","intvolume":" 22","scopus_import":"1","file":[{"date_updated":"2022-05-12T12:50:27Z","file_size":1162454,"creator":"dernst","date_created":"2022-05-12T12:50:27Z","file_name":"2021_AnnHenriPoincare_Erdoes.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"11365","checksum":"8d6bac0e2b0a28539608b0538a8e3b38","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"publication_status":"published","volume":22,"ec_funded":1,"project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269.","chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum Dots via Noncommutative Rational Functions.” Annales Henri Poincaré . Springer Nature, 2021. https://doi.org/10.1007/s00023-021-01085-6.","apa":"Erdös, L., Krüger, T. H., & Nemish, Y. (2021). Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . Springer Nature. https://doi.org/10.1007/s00023-021-01085-6","ama":"Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 2021;22:4205–4269. doi:10.1007/s00023-021-01085-6","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative rational functions,” Annales Henri Poincaré , vol. 22. Springer Nature, pp. 4205–4269, 2021.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269.","mla":"Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational Functions.” Annales Henri Poincaré , vol. 22, Springer Nature, 2021, pp. 4205–4269, doi:10.1007/s00023-021-01085-6."},"title":"Scattering in quantum dots via noncommutative rational functions","author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Nemish","full_name":"Nemish, Yuriy","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy"}],"external_id":{"arxiv":["1911.05112"],"isi":["000681531500001"]},"article_processing_charge":"Yes (in subscription journal)","acknowledgement":"The authors are very grateful to Yan Fyodorov for discussions on the physical background and for providing references, and to the anonymous referee for numerous valuable remarks.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"day":"01","publication":"Annales Henri Poincaré ","has_accepted_license":"1","isi":1,"year":"2021","doi":"10.1007/s00023-021-01085-6","date_published":"2021-12-01T00:00:00Z","date_created":"2021-08-15T22:01:29Z","page":"4205–4269"},{"year":"2021","isi":1,"has_accepted_license":"1","publication":"Communications in Mathematical Physics","day":"29","page":"1005–1048","date_created":"2021-11-07T23:01:25Z","date_published":"2021-10-29T00:00:00Z","doi":"10.1007/s00220-021-04239-z","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","oa":1,"publisher":"Springer Nature","quality_controlled":"1","citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis for Wigner matrices,” Communications in Mathematical Physics, vol. 388, no. 2. Springer Nature, pp. 1005–1048, 2021.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04239-z","ama":"Cipolloni G, Erdös L, Schröder DJ. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 2021;388(2):1005–1048. doi:10.1007/s00220-021-04239-z","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” Communications in Mathematical Physics, vol. 388, no. 2, Springer Nature, 2021, pp. 1005–1048, doi:10.1007/s00220-021-04239-z.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04239-z."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000712232700001"],"arxiv":["2012.13215"]},"author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"title":"Eigenstate thermalization hypothesis for Wigner matrices","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publication_status":"published","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"language":[{"iso":"eng"}],"file":[{"creator":"cchlebak","date_updated":"2022-02-02T10:19:55Z","file_size":841426,"date_created":"2022-02-02T10:19:55Z","file_name":"2021_CommunMathPhys_Cipolloni.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"a2c7b6f5d23b5453cd70d1261272283b","file_id":"10715","success":1}],"volume":388,"issue":"2","abstract":[{"text":"We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 388","month":"10","date_updated":"2023-08-14T10:29:49Z","ddc":["510"],"department":[{"_id":"LaEr"}],"file_date_updated":"2022-02-02T10:19:55Z","_id":"10221","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public"},{"file_date_updated":"2021-01-25T14:19:10Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"supervisor":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"}],"date_updated":"2023-09-07T13:29:32Z","ddc":["510"],"type":"dissertation","status":"public","_id":"9022","ec_funded":1,"publication_identifier":{"issn":["2663-337X"]},"degree_awarded":"PhD","publication_status":"published","file":[{"file_name":"thesis.pdf","date_created":"2021-01-25T14:19:03Z","creator":"gcipollo","file_size":4127796,"date_updated":"2021-01-25T14:19:03Z","success":1,"checksum":"5a93658a5f19478372523ee232887e2b","file_id":"9043","relation":"main_file","access_level":"open_access","content_type":"application/pdf"},{"creator":"gcipollo","date_updated":"2021-01-25T14:19:10Z","file_size":12775206,"date_created":"2021-01-25T14:19:10Z","file_name":"Thesis_files.zip","access_level":"closed","relation":"source_file","content_type":"application/zip","file_id":"9044","checksum":"e8270eddfe6a988e92a53c88d1d19b8c"}],"language":[{"iso":"eng"}],"alternative_title":["ISTA Thesis"],"month":"01","abstract":[{"lang":"eng","text":"In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample covariance matrices XX∗ with X having independent identically distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences of linear statistics of XX∗ and its minor after removing the first column of X. Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics near cusp singularities of the limiting density of states are universal and that they form a Pearcey process. Since the limiting eigenvalue distribution admits only square root (edge) and cubic root (cusp) singularities, this concludes the third and last remaining case of the Wigner-Dyson-Mehta universality conjecture. The main technical ingredients are an optimal local law at the cusp, and the proof of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp regime.\r\nIn the second part we consider non-Hermitian matrices X with centred i.i.d. entries. We normalise the entries of X to have variance N −1. It is well known that the empirical eigenvalue density converges to the uniform distribution on the unit disk (circular law). In the first project, we prove universality of the local eigenvalue statistics close to the edge of the spectrum. This is the non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck flow for very long time\r\n(up to t = +∞). In the second project, we consider linear statistics of eigenvalues for macroscopic test functions f in the Sobolev space H2+ϵ and prove their convergence to the projection of the Gaussian Free Field on the unit disk. We prove this result for non-Hermitian matrices with real or complex entries. The main technical ingredients are: (i) local law for products of two resolvents at different spectral parameters, (ii) analysis of correlated Dyson Brownian motions.\r\nIn the third and final part we discuss the mathematically rigorous application of supersymmetric techniques (SUSY ) to give a lower tail estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we use superbosonisation formula to give an integral representation of the resolvent of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex and real case, respectively. The rigorous analysis of these integrals is quite challenging since simple saddle point analysis cannot be applied (the main contribution comes from a non-trivial manifold). Our result\r\nimproves classical smoothing inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality for i.i.d. non-Hermitian matrices."}],"oa_version":"Published Version","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","title":"Fluctuations in the spectrum of random matrices","citation":{"ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria.","chicago":"Cipolloni, Giorgio. “Fluctuations in the Spectrum of Random Matrices.” Institute of Science and Technology Austria, 2021. https://doi.org/10.15479/AT:ISTA:9022.","ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi:10.15479/AT:ISTA:9022","apa":"Cipolloni, G. (2021). Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:9022","short":"G. Cipolloni, Fluctuations in the Spectrum of Random Matrices, Institute of Science and Technology Austria, 2021.","ieee":"G. Cipolloni, “Fluctuations in the spectrum of random matrices,” Institute of Science and Technology Austria, 2021.","mla":"Cipolloni, Giorgio. Fluctuations in the Spectrum of Random Matrices. Institute of Science and Technology Austria, 2021, doi:10.15479/AT:ISTA:9022."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385"},{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"page":"380","date_published":"2021-01-25T00:00:00Z","doi":"10.15479/AT:ISTA:9022","date_created":"2021-01-21T18:16:54Z","has_accepted_license":"1","year":"2021","day":"25","publisher":"Institute of Science and Technology Austria","oa":1,"acknowledgement":"I gratefully acknowledge the financial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 665385 and my advisor’s ERC Advanced Grant No. 338804."},{"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1907.13631"}],"scopus_import":"1","intvolume":" 2","month":"05","abstract":[{"text":"We consider random n×n matrices X with independent and centered entries and a general variance profile. We show that the spectral radius of X converges with very high probability to the square root of the spectral radius of the variance matrix of X when n tends to infinity. We also establish the optimal rate of convergence, that is a new result even for general i.i.d. matrices beyond the explicitly solvable Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular law [arXiv:1612.07776] at the spectral edge.","lang":"eng"}],"oa_version":"Preprint","ec_funded":1,"volume":2,"issue":"2","publication_status":"published","publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"language":[{"iso":"eng"}],"type":"journal_article","article_type":"original","status":"public","_id":"15013","department":[{"_id":"LaEr"}],"date_updated":"2024-02-19T08:30:00Z","oa":1,"publisher":"Mathematical Sciences Publishers","quality_controlled":"1","acknowledgement":"Partially supported by ERC Starting Grant RandMat No. 715539 and the SwissMap grant of Swiss National Science Foundation. Partially supported by ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center for Mathematics in Bonn.","page":"221-280","date_created":"2024-02-18T23:01:03Z","date_published":"2021-05-21T00:00:00Z","doi":"10.2140/pmp.2021.2.221","year":"2021","publication":"Probability and Mathematical Physics","day":"21","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"external_id":{"arxiv":["1907.13631"]},"article_processing_charge":"No","author":[{"last_name":"Alt","full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger"}],"title":"Spectral radius of random matrices with independent entries","citation":{"mla":"Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent Entries.” Probability and Mathematical Physics, vol. 2, no. 2, Mathematical Sciences Publishers, 2021, pp. 221–80, doi:10.2140/pmp.2021.2.221.","apa":"Alt, J., Erdös, L., & Krüger, T. H. (2021). Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2021.2.221","ama":"Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2021;2(2):221-280. doi:10.2140/pmp.2021.2.221","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with independent entries,” Probability and Mathematical Physics, vol. 2, no. 2. Mathematical Sciences Publishers, pp. 221–280, 2021.","short":"J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021) 221–280.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random Matrices with Independent Entries.” Probability and Mathematical Physics. Mathematical Sciences Publishers, 2021. https://doi.org/10.2140/pmp.2021.2.221.","ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields. Springer Nature, 2021. https://doi.org/10.1007/s00440-020-01003-7.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.","mla":"Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, Springer Nature, 2021, doi:10.1007/s00440-020-01003-7.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 2021.","ama":"Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. 2021. doi:10.1007/s00440-020-01003-7","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-020-01003-7"},"title":"Edge universality for non-Hermitian random matrices","author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"external_id":{"arxiv":["1908.00969"],"isi":["000572724600002"]},"article_processing_charge":"Yes (via OA deal)","quality_controlled":"1","publisher":"Springer Nature","oa":1,"day":"01","publication":"Probability Theory and Related Fields","isi":1,"has_accepted_license":"1","year":"2021","date_published":"2021-02-01T00:00:00Z","doi":"10.1007/s00440-020-01003-7","date_created":"2020-10-04T22:01:37Z","_id":"8601","status":"public","article_type":"original","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"ddc":["510"],"date_updated":"2024-03-07T15:07:53Z","department":[{"_id":"LaEr"}],"file_date_updated":"2020-10-05T14:53:40Z","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble."}],"month":"02","scopus_import":"1","file":[{"checksum":"611ae28d6055e1e298d53a57beb05ef4","file_id":"8612","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2020-10-05T14:53:40Z","file_name":"2020_ProbTheory_Cipolloni.pdf","creator":"dernst","date_updated":"2020-10-05T14:53:40Z","file_size":497032}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"publication_status":"published","ec_funded":1},{"page":"5855-5883","date_created":"2020-01-29T10:20:46Z","doi":"10.1090/tran/8113","date_published":"2020-08-01T00:00:00Z","year":"2020","isi":1,"publication":"Transactions of the American Mathematical Society","day":"01","oa":1,"publisher":"American Mathematical Society","quality_controlled":"1","article_processing_charge":"No","external_id":{"arxiv":["2002.00859"],"isi":["000551418100018"]},"author":[{"first_name":"Gyorgy Pal","full_name":"Geher, Gyorgy Pal","last_name":"Geher"},{"last_name":"Titkos","full_name":"Titkos, Tamas","first_name":"Tamas"},{"first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511"}],"title":"Isometric study of Wasserstein spaces - the real line","citation":{"ista":"Geher GP, Titkos T, Virosztek D. 2020. Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. 373(8), 5855–5883.","chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study of Wasserstein Spaces - the Real Line.” Transactions of the American Mathematical Society. American Mathematical Society, 2020. https://doi.org/10.1090/tran/8113.","short":"G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society 373 (2020) 5855–5883.","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Isometric study of Wasserstein spaces - the real line,” Transactions of the American Mathematical Society, vol. 373, no. 8. American Mathematical Society, pp. 5855–5883, 2020.","ama":"Geher GP, Titkos T, Virosztek D. Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. 2020;373(8):5855-5883. doi:10.1090/tran/8113","apa":"Geher, G. P., Titkos, T., & Virosztek, D. (2020). Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. American Mathematical Society. https://doi.org/10.1090/tran/8113","mla":"Geher, Gyorgy Pal, et al. “Isometric Study of Wasserstein Spaces - the Real Line.” Transactions of the American Mathematical Society, vol. 373, no. 8, American Mathematical Society, 2020, pp. 5855–83, doi:10.1090/tran/8113."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"ec_funded":1,"volume":373,"issue":"8","publication_status":"published","publication_identifier":{"issn":["00029947"],"eissn":["10886850"]},"language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.00859"}],"intvolume":" 373","month":"08","abstract":[{"text":"Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space W_2(R^n). It turned out that the case of the real line is exceptional in the sense that there exists an exotic isometry flow. Following this line of investigation, we compute Isom(W_p(R)), the isometry group of the Wasserstein space\r\nW_p(R) for all p \\in [1,\\infty) \\setminus {2}. We show that W_2(R) is also exceptional regarding the\r\nparameter p: W_p(R) is isometrically rigid if and only if p is not equal to 2. Regarding the underlying\r\nspace, we prove that the exceptionality of p = 2 disappears if we replace R by the compact\r\ninterval [0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only if\r\np is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass, and Isom(W_1([0,1]))\r\ncannot be embedded into Isom(W_1(R)).","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"LaEr"}],"date_updated":"2023-08-17T14:31:03Z","ddc":["515"],"article_type":"original","type":"journal_article","keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"status":"public","_id":"7389"},{"issue":"12","volume":278,"ec_funded":1,"publication_identifier":{"eissn":["10960783"],"issn":["00221236"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1804.11340","open_access":"1"}],"month":"07","intvolume":" 278","abstract":[{"text":"We consider general self-adjoint polynomials in several independent random matrices whose entries are centered and have the same variance. We show that under certain conditions the local law holds up to the optimal scale, i.e., the eigenvalue density on scales just above the eigenvalue spacing follows the global density of states which is determined by free probability theory. We prove that these conditions hold for general homogeneous polynomials of degree two and for symmetrized products of independent matrices with i.i.d. entries, thus establishing the optimal bulk local law for these classes of ensembles. In particular, we generalize a similar result of Anderson for anticommutator. For more general polynomials our conditions are effectively checkable numerically.","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"LaEr"}],"date_updated":"2023-08-18T06:36:10Z","article_type":"original","type":"journal_article","status":"public","_id":"7512","doi":"10.1016/j.jfa.2020.108507","date_published":"2020-07-01T00:00:00Z","date_created":"2020-02-23T23:00:36Z","isi":1,"year":"2020","day":"01","publication":"Journal of Functional Analysis","quality_controlled":"1","publisher":"Elsevier","oa":1,"acknowledgement":"The authors are grateful to Oskari Ajanki for his invaluable help at the initial stage of this project, to Serban Belinschi for useful discussions, to Alexander Tikhomirov for calling our attention to the model example in Section 6.2 and to the anonymous referee for suggesting to simplify certain proofs. Erdös: Partially funded by ERC Advanced Grant RANMAT No. 338804\r\n","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"last_name":"Krüger","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy","last_name":"Nemish","orcid":"0000-0002-7327-856X","full_name":"Nemish, Yuriy"}],"external_id":{"isi":["000522798900001"],"arxiv":["1804.11340"]},"article_processing_charge":"No","title":"Local laws for polynomials of Wigner matrices","citation":{"chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Local Laws for Polynomials of Wigner Matrices.” Journal of Functional Analysis. Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108507.","ista":"Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 278(12), 108507.","mla":"Erdös, László, et al. “Local Laws for Polynomials of Wigner Matrices.” Journal of Functional Analysis, vol. 278, no. 12, 108507, Elsevier, 2020, doi:10.1016/j.jfa.2020.108507.","apa":"Erdös, L., Krüger, T. H., & Nemish, Y. (2020). Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2020.108507","ama":"Erdös L, Krüger TH, Nemish Y. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 2020;278(12). doi:10.1016/j.jfa.2020.108507","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner matrices,” Journal of Functional Analysis, vol. 278, no. 12. Elsevier, 2020.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020)."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"article_number":"108507"},{"abstract":[{"lang":"eng","text":"This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger divergences that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to the family of maximal quantum f-divergences, and hence are jointly convex, and satisfy the data processing inequality. We derive a characterization of the barycenter of finitely many positive definite operators for these generalized quantum Hellinger divergences. We note that the characterization of the barycenter as the weighted multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true in the case of commuting operators, but it is not correct in the general case. "}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.10455"}],"month":"08","intvolume":" 110","publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"8","volume":110,"ec_funded":1,"_id":"7618","type":"journal_article","article_type":"original","status":"public","date_updated":"2023-08-18T10:17:26Z","department":[{"_id":"LaEr"}],"acknowledgement":"J. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant for Quantum\r\nInformation Theory, No. 96 141, and by the Hungarian National Research, Development and Innovation\r\nOffice (NKFIH) via Grants Nos. K119442, K124152 and KH129601. D. Virosztek was supported by the\r\nISTFELLOW program of the Institute of Science and Technology Austria (Project Code IC1027FELL01),\r\nby the European Union’s Horizon 2020 research and innovation program under the Marie\r\nSklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National\r\nResearch, Development and Innovation Office (NKFIH) via Grants Nos. K124152 and KH129601.\r\nWe are grateful to Milán Mosonyi for drawing our attention to Ref.’s [6,14,15,17,\r\n20,21], for comments on earlier versions of this paper, and for several discussions on the topic. We are\r\nalso grateful to Miklós Pálfia for several discussions; to László Erdös for his essential suggestions on the\r\nstructure and highlights of this paper, and for his comments on earlier versions; and to the anonymous\r\nreferee for his/her valuable comments and suggestions.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"isi":1,"year":"2020","day":"01","publication":"Letters in Mathematical Physics","page":"2039-2052","doi":"10.1007/s11005-020-01282-0","date_published":"2020-08-01T00:00:00Z","date_created":"2020-03-25T15:57:48Z","project":[{"call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425","name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294"},{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"citation":{"chicago":"Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.” Letters in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s11005-020-01282-0.","ista":"Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 110(8), 2039–2052.","mla":"Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.” Letters in Mathematical Physics, vol. 110, no. 8, Springer Nature, 2020, pp. 2039–52, doi:10.1007/s11005-020-01282-0.","ama":"Pitrik J, Virosztek D. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 2020;110(8):2039-2052. doi:10.1007/s11005-020-01282-0","apa":"Pitrik, J., & Virosztek, D. (2020). Quantum Hellinger distances revisited. Letters in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s11005-020-01282-0","short":"J. Pitrik, D. Virosztek, Letters in Mathematical Physics 110 (2020) 2039–2052.","ieee":"J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” Letters in Mathematical Physics, vol. 110, no. 8. Springer Nature, pp. 2039–2052, 2020."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Jozsef","full_name":"Pitrik, Jozsef","last_name":"Pitrik"},{"orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel"}],"article_processing_charge":"No","external_id":{"arxiv":["1903.10455"],"isi":["000551556000002"]},"title":"Quantum Hellinger distances revisited"},{"department":[{"_id":"LaEr"}],"date_updated":"2023-08-24T11:16:03Z","status":"public","article_type":"original","type":"journal_article","_id":"9104","ec_funded":1,"volume":142,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["15658538"],"issn":["00217670"]},"intvolume":" 142","month":"11","main_file_link":[{"url":"https://arxiv.org/abs/1804.11199","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider the free additive convolution of two probability measures μ and ν on the real line and show that μ ⊞ v is supported on a single interval if μ and ν each has single interval support. Moreover, the density of μ ⊞ ν is proven to vanish as a square root near the edges of its support if both μ and ν have power law behavior with exponents between −1 and 1 near their edges. In particular, these results show the ubiquity of the conditions in our recent work on optimal local law at the spectral edges for addition of random matrices [5]."}],"title":"On the support of the free additive convolution","external_id":{"arxiv":["1804.11199"],"isi":["000611879400008"]},"article_processing_charge":"No","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","last_name":"Bao"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Bao, Zhigang, et al. “On the Support of the Free Additive Convolution.” Journal d’Analyse Mathematique, vol. 142, Springer Nature, 2020, pp. 323–48, doi:10.1007/s11854-020-0135-2.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,” Journal d’Analyse Mathematique, vol. 142. Springer Nature, pp. 323–348, 2020.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348.","ama":"Bao Z, Erdös L, Schnelli K. On the support of the free additive convolution. Journal d’Analyse Mathematique. 2020;142:323-348. doi:10.1007/s11854-020-0135-2","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2020). On the support of the free additive convolution. Journal d’Analyse Mathematique. Springer Nature. https://doi.org/10.1007/s11854-020-0135-2","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “On the Support of the Free Additive Convolution.” Journal d’Analyse Mathematique. Springer Nature, 2020. https://doi.org/10.1007/s11854-020-0135-2.","ista":"Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 323–348."},"project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"date_created":"2021-02-07T23:01:15Z","date_published":"2020-11-01T00:00:00Z","doi":"10.1007/s11854-020-0135-2","page":"323-348","publication":"Journal d'Analyse Mathematique","day":"01","year":"2020","isi":1,"oa":1,"quality_controlled":"1","publisher":"Springer Nature","acknowledgement":"Supported in part by Hong Kong RGC Grant ECS 26301517.\r\nSupported in part by ERC Advanced Grant RANMAT No. 338804.\r\nSupported in part by the Knut and Alice Wallenberg Foundation and the Swedish Research Council Grant VR-2017-05195."},{"year":"2020","isi":1,"publication":"Journal of Functional Analysis","day":"15","date_created":"2022-03-18T10:18:59Z","doi":"10.1016/j.jfa.2020.108639","date_published":"2020-10-15T00:00:00Z","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804.","oa":1,"publisher":"Elsevier","quality_controlled":"1","citation":{"short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random matrices at the regular edge,” Journal of Functional Analysis, vol. 279, no. 7. Elsevier, 2020.","ama":"Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 2020;279(7). doi:10.1016/j.jfa.2020.108639","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2020). Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2020.108639","mla":"Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” Journal of Functional Analysis, vol. 279, no. 7, 108639, Elsevier, 2020, doi:10.1016/j.jfa.2020.108639.","ista":"Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” Journal of Functional Analysis. Elsevier, 2020. https://doi.org/10.1016/j.jfa.2020.108639."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"arxiv":["1708.01597"],"isi":["000559623200009"]},"article_processing_charge":"No","author":[{"last_name":"Bao","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"first_name":"Kevin","last_name":"Schnelli","full_name":"Schnelli, Kevin"}],"title":"Spectral rigidity for addition of random matrices at the regular edge","article_number":"108639","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"publication_status":"published","publication_identifier":{"issn":["0022-1236"]},"language":[{"iso":"eng"}],"ec_funded":1,"volume":279,"issue":"7","abstract":[{"lang":"eng","text":"We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu's theorem. Our previous works [4], [5] established these results in the bulk spectrum, the current paper completely settles the problem at the spectral edges provided they have the typical square-root behavior. The key element of our proof is to compensate the deterioration of the stability of the subordination equations by sharp error estimates that properly account for the local density near the edge. Our results also hold if the Haar unitary matrix is replaced by the Haar orthogonal matrix."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01597"}],"scopus_import":"1","intvolume":" 279","month":"10","date_updated":"2023-08-24T14:08:42Z","department":[{"_id":"LaEr"}],"_id":"10862","article_type":"original","type":"journal_article","keyword":["Analysis"],"status":"public"},{"date_updated":"2023-08-28T08:38:48Z","department":[{"_id":"LaEr"}],"_id":"6488","type":"journal_article","article_type":"original","status":"public","publication_identifier":{"issn":["20103263"],"eissn":["20103271"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"3","volume":9,"ec_funded":1,"abstract":[{"text":"We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish.","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1806.08751"}],"month":"07","intvolume":" 9","citation":{"ista":"Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 9(3), 2050006.","chicago":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application. World Scientific Publishing, 2020. https://doi.org/10.1142/S2010326320500069.","ama":"Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 2020;9(3). doi:10.1142/S2010326320500069","apa":"Cipolloni, G., & Erdös, L. (2020). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. World Scientific Publishing. https://doi.org/10.1142/S2010326320500069","short":"G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).","ieee":"G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” Random Matrices: Theory and Application, vol. 9, no. 3. World Scientific Publishing, 2020.","mla":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” Random Matrices: Theory and Application, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020, doi:10.1142/S2010326320500069."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"}],"article_processing_charge":"No","external_id":{"arxiv":["1806.08751"],"isi":["000547464400001"]},"title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","article_number":"2050006","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"isi":1,"year":"2020","day":"01","publication":"Random Matrices: Theory and Application","doi":"10.1142/S2010326320500069","date_published":"2020-07-01T00:00:00Z","date_created":"2019-05-26T21:59:14Z","quality_controlled":"1","publisher":"World Scientific Publishing","oa":1},{"file_date_updated":"2020-11-18T11:14:37Z","department":[{"_id":"LaEr"}],"ddc":["530","510"],"date_updated":"2023-09-07T12:54:12Z","status":"public","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"6185","related_material":{"record":[{"id":"6179","status":"public","relation":"dissertation_contains"}]},"volume":378,"ec_funded":1,"file":[{"creator":"dernst","date_updated":"2020-11-18T11:14:37Z","file_size":2904574,"date_created":"2020-11-18T11:14:37Z","file_name":"2020_CommMathPhysics_Erdoes.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"8771","checksum":"c3a683e2afdcea27afa6880b01e53dc2","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"publication_status":"published","month":"09","intvolume":" 378","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969)."}],"title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","author":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000529483000001"],"arxiv":["1809.03971"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 378, 1203–1278.","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications in Mathematical Physics. Springer Nature, 2020. https://doi.org/10.1007/s00220-019-03657-4.","apa":"Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03657-4","ama":"Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 2020;378:1203-1278. doi:10.1007/s00220-019-03657-4","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” Communications in Mathematical Physics, vol. 378. Springer Nature, pp. 1203–1278, 2020.","mla":"Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” Communications in Mathematical Physics, vol. 378, Springer Nature, 2020, pp. 1203–78, doi:10.1007/s00220-019-03657-4."},"project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"doi":"10.1007/s00220-019-03657-4","date_published":"2020-09-01T00:00:00Z","date_created":"2019-03-28T10:21:15Z","page":"1203-1278","day":"01","publication":"Communications in Mathematical Physics","isi":1,"has_accepted_license":"1","year":"2020","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to Johannes Alt for numerous discussions on the Dyson equation and for his invaluable help in adjusting [10] to the needs of the present work."},{"ddc":["510"],"date_updated":"2023-12-18T10:46:09Z","file_date_updated":"2023-12-18T10:42:32Z","department":[{"_id":"LaEr"}],"_id":"14694","keyword":["General Mathematics"],"status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","language":[{"iso":"eng"}],"file":[{"file_name":"2020_DocumentaMathematica_Alt.pdf","date_created":"2023-12-18T10:42:32Z","file_size":1374708,"date_updated":"2023-12-18T10:42:32Z","creator":"dernst","success":1,"file_id":"14695","checksum":"12aacc1d63b852ff9a51c1f6b218d4a6","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"publication_status":"published","publication_identifier":{"eissn":["1431-0643"],"issn":["1431-0635"]},"volume":25,"related_material":{"record":[{"relation":"earlier_version","id":"6183","status":"public"}]},"oa_version":"Published Version","abstract":[{"text":"We study the unique solution m of the Dyson equation \\( -m(z)^{-1} = z\\1 - a + S[m(z)] \\) on a von Neumann algebra A with the constraint Imm≥0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of A and S is a positivity-preserving linear operator on A. We show that m is the Stieltjes transform of a compactly supported A-valued measure on R. Under suitable assumptions, we establish that this measure has a uniformly 1/3-Hölder continuous density with respect to the Lebesgue measure, which is supported on finitely many intervals, called bands. In fact, the density is analytic inside the bands with a square-root growth at the edges and internal cubic root cusps whenever the gap between two bands vanishes. The shape of these singularities is universal and no other singularity may occur. We give a precise asymptotic description of m near the singular points. These asymptotics generalize the analysis at the regular edges given in the companion paper on the Tracy-Widom universality for the edge eigenvalue statistics for correlated random matrices [the first author et al., Ann. Probab. 48, No. 2, 963--1001 (2020; Zbl 1434.60017)] and they play a key role in the proof of the Pearcey universality at the cusp for Wigner-type matrices [G. Cipolloni et al., Pure Appl. Anal. 1, No. 4, 615--707 (2019; Zbl 07142203); the second author et al., Commun. Math. Phys. 378, No. 2, 1203--1278 (2020; Zbl 07236118)]. We also extend the finite dimensional band mass formula from [the first author et al., loc. cit.] to the von Neumann algebra setting by showing that the spectral mass of the bands is topologically rigid under deformations and we conclude that these masses are quantized in some important cases.","lang":"eng"}],"intvolume":" 25","month":"09","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Alt J, Erdös L, Krüger TH. 2020. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 25, 1421–1539.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica. EMS Press, 2020. https://doi.org/10.4171/dm/780.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” Documenta Mathematica, vol. 25. EMS Press, pp. 1421–1539, 2020.","short":"J. Alt, L. Erdös, T.H. Krüger, Documenta Mathematica 25 (2020) 1421–1539.","ama":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 2020;25:1421-1539. doi:10.4171/dm/780","apa":"Alt, J., Erdös, L., & Krüger, T. H. (2020). The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. EMS Press. https://doi.org/10.4171/dm/780","mla":"Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” Documenta Mathematica, vol. 25, EMS Press, 2020, pp. 1421–539, doi:10.4171/dm/780."},"title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","article_processing_charge":"Yes","external_id":{"arxiv":["1804.07752"]},"author":[{"full_name":"Alt, Johannes","last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"publication":"Documenta Mathematica","day":"01","year":"2020","has_accepted_license":"1","date_created":"2023-12-18T10:37:43Z","date_published":"2020-09-01T00:00:00Z","doi":"10.4171/dm/780","page":"1421-1539","oa":1,"quality_controlled":"1","publisher":"EMS Press"},{"_id":"6184","type":"journal_article","article_type":"original","status":"public","date_updated":"2024-02-22T14:34:33Z","department":[{"_id":"LaEr"}],"abstract":[{"text":"We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.07744"}],"month":"03","intvolume":" 48","publication_identifier":{"issn":["0091-1798"]},"publication_status":"published","language":[{"iso":"eng"}],"related_material":{"record":[{"relation":"dissertation_contains","id":"149","status":"public"},{"relation":"dissertation_contains","status":"public","id":"6179"}]},"volume":48,"issue":"2","ec_funded":1,"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"citation":{"chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder. “Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of Probability. Institute of Mathematical Statistics, 2020. https://doi.org/10.1214/19-AOP1379.","ista":"Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.","mla":"Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge Universality.” Annals of Probability, vol. 48, no. 2, Institute of Mathematical Statistics, 2020, pp. 963–1001, doi:10.1214/19-AOP1379.","ama":"Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 2020;48(2):963-1001. doi:10.1214/19-AOP1379","apa":"Alt, J., Erdös, L., Krüger, T. H., & Schröder, D. J. (2020). Correlated random matrices: Band rigidity and edge universality. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/19-AOP1379","ieee":"J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” Annals of Probability, vol. 48, no. 2. Institute of Mathematical Statistics, pp. 963–1001, 2020.","short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes","last_name":"Alt"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger"},{"orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"external_id":{"arxiv":["1804.07744"],"isi":["000528269100013"]},"article_processing_charge":"No","title":"Correlated random matrices: Band rigidity and edge universality","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"isi":1,"year":"2020","day":"01","publication":"Annals of Probability","page":"963-1001","date_published":"2020-03-01T00:00:00Z","doi":"10.1214/19-AOP1379","date_created":"2019-03-28T09:20:08Z"},{"oa":1,"quality_controlled":"1","publisher":"Mathematical Sciences Publishers","acknowledgement":"Partially supported by ERC Advanced Grant No. 338804. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 66538","date_created":"2024-03-04T10:27:57Z","date_published":"2020-11-16T00:00:00Z","doi":"10.2140/pmp.2020.1.101","page":"101-146","publication":"Probability and Mathematical Physics","day":"16","year":"2020","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"title":"Optimal lower bound on the least singular value of the shifted Ginibre ensemble","article_processing_charge":"No","external_id":{"arxiv":["1908.01653"]},"author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2020. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. 1(1), 101–146.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” Probability and Mathematical Physics. Mathematical Sciences Publishers, 2020. https://doi.org/10.2140/pmp.2020.1.101.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability and Mathematical Physics 1 (2020) 101–146.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least singular value of the shifted Ginibre ensemble,” Probability and Mathematical Physics, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020.","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. 2020;1(1):101-146. doi:10.2140/pmp.2020.1.101","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2020). Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. Mathematical Sciences Publishers. https://doi.org/10.2140/pmp.2020.1.101","mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” Probability and Mathematical Physics, vol. 1, no. 1, Mathematical Sciences Publishers, 2020, pp. 101–46, doi:10.2140/pmp.2020.1.101."},"intvolume":" 1","month":"11","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1908.01653"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395)."}],"ec_funded":1,"volume":1,"issue":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["2690-1005","2690-0998"]},"keyword":["General Medicine"],"status":"public","article_type":"original","type":"journal_article","_id":"15063","department":[{"_id":"LaEr"}],"date_updated":"2024-03-04T10:33:15Z"},{"type":"journal_article","article_type":"original","status":"public","_id":"15079","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Friedrich","last_name":"Götze","full_name":"Götze, Friedrich"},{"full_name":"Guionnet, Alice","last_name":"Guionnet","first_name":"Alice"}],"article_processing_charge":"No","department":[{"_id":"LaEr"}],"title":"Random matrices","citation":{"ista":"Erdös L, Götze F, Guionnet A. 2020. Random matrices. Oberwolfach Reports. 16(4), 3459–3527.","chicago":"Erdös, László, Friedrich Götze, and Alice Guionnet. “Random Matrices.” Oberwolfach Reports. European Mathematical Society, 2020. https://doi.org/10.4171/owr/2019/56.","short":"L. Erdös, F. Götze, A. Guionnet, Oberwolfach Reports 16 (2020) 3459–3527.","ieee":"L. Erdös, F. Götze, and A. Guionnet, “Random matrices,” Oberwolfach Reports, vol. 16, no. 4. European Mathematical Society, pp. 3459–3527, 2020.","ama":"Erdös L, Götze F, Guionnet A. Random matrices. Oberwolfach Reports. 2020;16(4):3459-3527. doi:10.4171/owr/2019/56","apa":"Erdös, L., Götze, F., & Guionnet, A. (2020). Random matrices. Oberwolfach Reports. European Mathematical Society. https://doi.org/10.4171/owr/2019/56","mla":"Erdös, László, et al. “Random Matrices.” Oberwolfach Reports, vol. 16, no. 4, European Mathematical Society, 2020, pp. 3459–527, doi:10.4171/owr/2019/56."},"date_updated":"2024-03-12T12:25:18Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"European Mathematical Society","quality_controlled":"1","month":"11","intvolume":" 16","abstract":[{"lang":"eng","text":"Large complex systems tend to develop universal patterns that often represent their essential characteristics. For example, the cumulative effects of independent or weakly dependent random variables often yield the Gaussian universality class via the central limit theorem. For non-commutative random variables, e.g. matrices, the Gaussian behavior is often replaced by another universality class, commonly called random matrix statistics. Nearby eigenvalues are strongly correlated, and, remarkably, their correlation structure is universal, depending only on the symmetry type of the matrix. Even more surprisingly, this feature is not restricted to matrices; in fact Eugene Wigner, the pioneer of the field, discovered in the 1950s that distributions of the gaps between energy levels of complicated quantum systems universally follow the same random matrix statistics. This claim has never been rigorously proved for any realistic physical system but experimental data and extensive numerics leave no doubt as to its correctness. Since then random matrices have proved to be extremely useful phenomenological models in a wide range of applications beyond quantum physics that include number theory, statistics, neuroscience, population dynamics, wireless communication and mathematical finance. The ubiquity of random matrices in natural sciences is still a mystery, but recent years have witnessed a breakthrough in the mathematical description of the statistical structure of their spectrum. Random matrices and closely related areas such as log-gases have become an extremely active research area in probability theory.\r\nThis workshop brought together outstanding researchers from a variety of mathematical backgrounds whose areas of research are linked to random matrices. While there are strong links between their motivations, the techniques used by these researchers span a large swath of mathematics, ranging from purely algebraic techniques to stochastic analysis, classical probability theory, operator algebra, supersymmetry, orthogonal polynomials, etc."}],"oa_version":"None","page":"3459-3527","date_published":"2020-11-19T00:00:00Z","volume":16,"doi":"10.4171/owr/2019/56","issue":"4","date_created":"2024-03-05T07:54:44Z","publication_identifier":{"issn":["1660-8933"]},"year":"2020","publication_status":"published","day":"19","publication":"Oberwolfach Reports","language":[{"iso":"eng"}]},{"day":"30","language":[{"iso":"eng"}],"publication":"Kyoto RIMS Kôkyûroku","publication_status":"published","year":"2019","date_published":"2019-01-30T00:00:00Z","volume":2125,"date_created":"2019-11-18T15:39:53Z","page":"34-41","oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"The aim of this short note is to expound one particular issue that was discussed during the talk [10] given at the symposium ”Researches on isometries as preserver problems and related topics” at Kyoto RIMS. That is, the role of Dirac masses by describing the isometry group of various metric spaces of probability measures. This article is of survey character, and it does not contain any essentially new results.From an isometric point of view, in some cases, metric spaces of measures are similar to C(K)-type function spaces. Similarity means here that their isometries are driven by some nice transformations of the underlying space. Of course, it depends on the particular choice of the metric how nice these transformations should be. Sometimes, as we will see, being a homeomorphism is enough to generate an isometry. But sometimes we need more: the transformation must preserve the underlying distance as well. Statements claiming that isometries in questions are necessarily induced by homeomorphisms are called Banach-Stone-type results, while results asserting that the underlying transformation is necessarily an isometry are termed as isometric rigidity results.As Dirac masses can be considered as building bricks of the set of all Borel measures, a natural question arises:Is it enough to understand how an isometry acts on the set of Dirac masses? Does this action extend uniquely to all measures?In what follows, we will thoroughly investigate this question."}],"month":"01","intvolume":" 2125","quality_controlled":"1","publisher":"Research Institute for Mathematical Sciences, Kyoto University","main_file_link":[{"open_access":"1","url":"http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"G.P. Geher, T. Titkos, D. Virosztek, in:, Kyoto RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41.","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Dirac masses and isometric rigidity,” in Kyoto RIMS Kôkyûroku, Kyoto, Japan, 2019, vol. 2125, pp. 34–41.","apa":"Geher, G. P., Titkos, T., & Virosztek, D. (2019). Dirac masses and isometric rigidity. In Kyoto RIMS Kôkyûroku (Vol. 2125, pp. 34–41). Kyoto, Japan: Research Institute for Mathematical Sciences, Kyoto University.","ama":"Geher GP, Titkos T, Virosztek D. Dirac masses and isometric rigidity. In: Kyoto RIMS Kôkyûroku. Vol 2125. Research Institute for Mathematical Sciences, Kyoto University; 2019:34-41.","mla":"Geher, Gyorgy Pal, et al. “Dirac Masses and Isometric Rigidity.” Kyoto RIMS Kôkyûroku, vol. 2125, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41.","ista":"Geher GP, Titkos T, Virosztek D. 2019. Dirac masses and isometric rigidity. Kyoto RIMS Kôkyûroku. Research on isometries as preserver problems and related topics vol. 2125, 34–41.","chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Dirac Masses and Isometric Rigidity.” In Kyoto RIMS Kôkyûroku, 2125:34–41. Research Institute for Mathematical Sciences, Kyoto University, 2019."},"date_updated":"2021-01-12T08:11:33Z","department":[{"_id":"LaEr"}],"title":"Dirac masses and isometric rigidity","author":[{"last_name":"Geher","full_name":"Geher, Gyorgy Pal","first_name":"Gyorgy Pal"},{"first_name":"Tamas","full_name":"Titkos, Tamas","last_name":"Titkos"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","last_name":"Virosztek"}],"article_processing_charge":"No","_id":"7035","status":"public","type":"conference","conference":{"start_date":"2019-01-28","location":"Kyoto, Japan","end_date":"2019-01-30","name":"Research on isometries as preserver problems and related topics"}},{"date_created":"2020-07-26T22:01:04Z","date_published":"2019-07-01T00:00:00Z","publication":"Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics","day":"01","year":"2019","oa":1,"quality_controlled":"1","publisher":"Formal Power Series and Algebraic Combinatorics","acknowledgement":"D.B. is especially grateful to Patrik Ferrari for suggesting simplifications in Section 3 and\r\nto Alessandra Occelli for suggesting the name for the models of Section 2.\r\n","title":"New edge asymptotics of skew Young diagrams via free boundaries","article_processing_charge":"No","external_id":{"arxiv":["1902.08750"]},"author":[{"first_name":"Dan","last_name":"Betea","full_name":"Betea, Dan"},{"last_name":"Bouttier","full_name":"Bouttier, Jérémie","first_name":"Jérémie"},{"first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","full_name":"Nejjar, Peter","last_name":"Nejjar"},{"first_name":"Mirjana","full_name":"Vuletíc, Mirjana","last_name":"Vuletíc"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Formal Power Series and Algebraic Combinatorics, 2019.","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of skew Young diagrams via free boundaries,” in Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Ljubljana, Slovenia, 2019.","ama":"Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young diagrams via free boundaries. In: Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Formal Power Series and Algebraic Combinatorics; 2019.","apa":"Betea, D., Bouttier, J., Nejjar, P., & Vuletíc, M. (2019). New edge asymptotics of skew Young diagrams via free boundaries. In Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Ljubljana, Slovenia: Formal Power Series and Algebraic Combinatorics.","mla":"Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, 34, Formal Power Series and Algebraic Combinatorics, 2019.","ista":"Betea D, Bouttier J, Nejjar P, Vuletíc M. 2019. New edge asymptotics of skew Young diagrams via free boundaries. Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics, 34.","chicago":"Betea, Dan, Jérémie Bouttier, Peter Nejjar, and Mirjana Vuletíc. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” In Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. Formal Power Series and Algebraic Combinatorics, 2019."},"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"article_number":"34","ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","month":"07","main_file_link":[{"url":"https://arxiv.org/abs/1902.08750","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng","text":"We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's problem on longest increasing subsequences of random permutations and the last passage percolation (corner growth) discrete versions thereof. Moreover they interpolate between said measures and the uniform measure on partitions. In the new KPZ-like 1/3 exponent edge scaling limit with logarithmic corrections, we find new probability distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions from the theory of random matrices."}],"department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T08:17:18Z","status":"public","conference":{"name":"FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics","end_date":"2019-07-05","location":"Ljubljana, Slovenia","start_date":"2019-07-01"},"type":"conference","_id":"8175"},{"scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1712.05324","open_access":"1"}],"month":"09","intvolume":" 576","abstract":[{"text":"We investigate the quantum Jensen divergences from the viewpoint of joint convexity. It turns out that the set of the functions which generate jointly convex quantum Jensen divergences on positive matrices coincides with the Matrix Entropy Class which has been introduced by Chen and Tropp quite recently.","lang":"eng"}],"oa_version":"Preprint","volume":576,"ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}],"type":"journal_article","article_type":"original","status":"public","_id":"405","department":[{"_id":"LaEr"}],"date_updated":"2023-08-24T14:31:47Z","quality_controlled":"1","publisher":"Elsevier","oa":1,"acknowledgement":"The author was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01) and partially supported by the Hungarian National Research, Development and Innovation Office – NKFIH (grant no. K124152)","page":"67-78","doi":"10.1016/j.laa.2018.03.002","date_published":"2019-09-01T00:00:00Z","date_created":"2018-12-11T11:46:17Z","isi":1,"year":"2019","day":"01","publication":"Linear Algebra and Its Applications","project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"publist_id":"7424","author":[{"full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","last_name":"Virosztek","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"arxiv":["1712.05324"],"isi":["000470955300005"]},"title":"Jointly convex quantum Jensen divergences","citation":{"mla":"Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” Linear Algebra and Its Applications, vol. 576, Elsevier, 2019, pp. 67–78, doi:10.1016/j.laa.2018.03.002.","short":"D. Virosztek, Linear Algebra and Its Applications 576 (2019) 67–78.","ieee":"D. Virosztek, “Jointly convex quantum Jensen divergences,” Linear Algebra and Its Applications, vol. 576. Elsevier, pp. 67–78, 2019.","apa":"Virosztek, D. (2019). Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2018.03.002","ama":"Virosztek D. Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. 2019;576:67-78. doi:10.1016/j.laa.2018.03.002","chicago":"Virosztek, Daniel. “Jointly Convex Quantum Jensen Divergences.” Linear Algebra and Its Applications. Elsevier, 2019. https://doi.org/10.1016/j.laa.2018.03.002.","ista":"Virosztek D. 2019. Jointly convex quantum Jensen divergences. Linear Algebra and Its Applications. 576, 67–78."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"page":"293–373","doi":"10.1007/s00440-018-0835-z","date_published":"2019-02-01T00:00:00Z","date_created":"2018-12-11T11:46:25Z","isi":1,"has_accepted_license":"1","year":"2019","day":"01","publication":"Probability Theory and Related Fields","publisher":"Springer","quality_controlled":"1","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\n","author":[{"id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","first_name":"Oskari H","last_name":"Ajanki","full_name":"Ajanki, Oskari H"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"last_name":"Krüger","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H"}],"publist_id":"7394","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000459396500007"]},"title":"Stability of the matrix Dyson equation and random matrices with correlations","citation":{"chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0835-z.","ista":"Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 173(1–2), 293–373.","mla":"Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields, vol. 173, no. 1–2, Springer, 2019, pp. 293–373, doi:10.1007/s00440-018-0835-z.","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation and random matrices with correlations,” Probability Theory and Related Fields, vol. 173, no. 1–2. Springer, pp. 293–373, 2019.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.","ama":"Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 2019;173(1-2):293–373. doi:10.1007/s00440-018-0835-z","apa":"Ajanki, O. H., Erdös, L., & Krüger, T. H. (2019). Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-018-0835-z"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"issue":"1-2","volume":173,"ec_funded":1,"publication_identifier":{"eissn":["14322064"],"issn":["01788051"]},"publication_status":"published","file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"5720","checksum":"f9354fa5c71f9edd17132588f0dc7d01","file_size":1201840,"date_updated":"2020-07-14T12:46:26Z","creator":"dernst","file_name":"2018_ProbTheory_Ajanki.pdf","date_created":"2018-12-17T16:12:08Z"}],"language":[{"iso":"eng"}],"scopus_import":"1","month":"02","intvolume":" 173","abstract":[{"text":"We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent.","lang":"eng"}],"oa_version":"Published Version","file_date_updated":"2020-07-14T12:46:26Z","department":[{"_id":"LaEr"}],"date_updated":"2023-08-24T14:39:00Z","ddc":["510"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","_id":"429"},{"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"citation":{"mla":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” Ergodic Theory and Dynamical Systems, vol. 39, no. 4, Cambridge University Press, 2019, pp. 1082–98, doi:10.1017/etds.2017.52.","ama":"Sadel C, Xu D. Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. 2019;39(4):1082-1098. doi:10.1017/etds.2017.52","apa":"Sadel, C., & Xu, D. (2019). Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. Cambridge University Press. https://doi.org/10.1017/etds.2017.52","ieee":"C. Sadel and D. Xu, “Singular analytic linear cocycles with negative infinite Lyapunov exponents,” Ergodic Theory and Dynamical Systems, vol. 39, no. 4. Cambridge University Press, pp. 1082–1098, 2019.","short":"C. Sadel, D. Xu, Ergodic Theory and Dynamical Systems 39 (2019) 1082–1098.","chicago":"Sadel, Christian, and Disheng Xu. “Singular Analytic Linear Cocycles with Negative Infinite Lyapunov Exponents.” Ergodic Theory and Dynamical Systems. Cambridge University Press, 2019. https://doi.org/10.1017/etds.2017.52.","ista":"Sadel C, Xu D. 2019. Singular analytic linear cocycles with negative infinite Lyapunov exponents. Ergodic Theory and Dynamical Systems. 39(4), 1082–1098."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"arxiv":["1601.06118"],"isi":["000459725600012"]},"article_processing_charge":"No","author":[{"orcid":"0000-0001-8255-3968","full_name":"Sadel, Christian","last_name":"Sadel","first_name":"Christian","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Disheng","full_name":"Xu, Disheng","last_name":"Xu"}],"title":"Singular analytic linear cocycles with negative infinite Lyapunov exponents","oa":1,"publisher":"Cambridge University Press","quality_controlled":"1","year":"2019","isi":1,"publication":"Ergodic Theory and Dynamical Systems","day":"01","page":"1082-1098","date_created":"2019-03-10T22:59:18Z","date_published":"2019-04-01T00:00:00Z","doi":"10.1017/etds.2017.52","_id":"6086","type":"journal_article","status":"public","date_updated":"2023-08-25T08:03:30Z","department":[{"_id":"LaEr"}],"abstract":[{"lang":"eng","text":"We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjugated to an upper triangular cocycle or a Jordan normal form. As a consequence, an arbitrarily small analytic perturbation leads to distinct Lyapunov exponents. Moreover, in the one-frequency case where the th Lyapunov exponent is finite and the st negative infinite, we obtain a simple criterion for domination in which case there is a splitting into a nilpotent part and an invertible part."}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1601.06118","open_access":"1"}],"scopus_import":"1","intvolume":" 39","month":"04","publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"issue":"4","volume":39},{"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"external_id":{"isi":["000466616100003"],"arxiv":["1612.05920"]},"article_processing_charge":"No","author":[{"orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","last_name":"Bao","first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"}],"title":"Local single ring theorem on optimal scale","citation":{"mla":"Bao, Zhigang, et al. “Local Single Ring Theorem on Optimal Scale.” Annals of Probability, vol. 47, no. 3, Institute of Mathematical Statistics, 2019, pp. 1270–334, doi:10.1214/18-AOP1284.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local single ring theorem on optimal scale,” Annals of Probability, vol. 47, no. 3. Institute of Mathematical Statistics, pp. 1270–1334, 2019.","short":"Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2019). Local single ring theorem on optimal scale. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AOP1284","ama":"Bao Z, Erdös L, Schnelli K. Local single ring theorem on optimal scale. Annals of Probability. 2019;47(3):1270-1334. doi:10.1214/18-AOP1284","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Single Ring Theorem on Optimal Scale.” Annals of Probability. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AOP1284.","ista":"Bao Z, Erdös L, Schnelli K. 2019. Local single ring theorem on optimal scale. Annals of Probability. 47(3), 1270–1334."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","page":"1270-1334","date_created":"2019-06-02T21:59:13Z","doi":"10.1214/18-AOP1284","date_published":"2019-05-01T00:00:00Z","year":"2019","isi":1,"publication":"Annals of Probability","day":"01","type":"journal_article","status":"public","_id":"6511","department":[{"_id":"LaEr"}],"date_updated":"2023-08-28T09:32:29Z","main_file_link":[{"url":"https://arxiv.org/abs/1612.05920","open_access":"1"}],"scopus_import":"1","intvolume":" 47","month":"05","abstract":[{"text":"Let U and V be two independent N by N random matrices that are distributed according to Haar measure on U(N). Let Σ be a nonnegative deterministic N by N matrix. The single ring theorem [Ann. of Math. (2) 174 (2011) 1189–1217] asserts that the empirical eigenvalue distribution of the matrix X:=UΣV∗ converges weakly, in the limit of large N, to a deterministic measure which is supported on a single ring centered at the origin in ℂ. Within the bulk regime, that is, in the interior of the single ring, we establish the convergence of the empirical eigenvalue distribution on the optimal local scale of order N−1/2+ε and establish the optimal convergence rate. The same results hold true when U and V are Haar distributed on O(N).","lang":"eng"}],"oa_version":"Preprint","ec_funded":1,"issue":"3","volume":47,"publication_status":"published","publication_identifier":{"issn":["00911798"]},"language":[{"iso":"eng"}]},{"issue":"2","volume":480,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022247X"],"eissn":["10960813"]},"publication_status":"published","month":"12","intvolume":" 480","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1809.01101","open_access":"1"}],"oa_version":"Preprint","abstract":[{"text":"The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space Wp(X), where S is a countable discrete metric space and 0
Journal of Mathematical Analysis and Applications. Elsevier, 2019. https://doi.org/10.1016/j.jmaa.2019.123435.","apa":"Gehér, G. P., Titkos, T., & Virosztek, D. (2019). On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. Elsevier. https://doi.org/10.1016/j.jmaa.2019.123435","ama":"Gehér GP, Titkos T, Virosztek D. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 2019;480(2). doi:10.1016/j.jmaa.2019.123435","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “On isometric embeddings of Wasserstein spaces – the discrete case,” Journal of Mathematical Analysis and Applications, vol. 480, no. 2. Elsevier, 2019.","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of Mathematical Analysis and Applications 480 (2019).","mla":"Gehér, György Pál, et al. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” Journal of Mathematical Analysis and Applications, vol. 480, no. 2, 123435, Elsevier, 2019, doi:10.1016/j.jmaa.2019.123435."},"project":[{"call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}],"article_number":"123435"},{"department":[{"_id":"LaEr"}],"date_updated":"2023-09-06T14:58:39Z","status":"public","article_type":"original","type":"journal_article","_id":"7423","volume":55,"issue":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0246-0203"]},"intvolume":" 55","month":"02","main_file_link":[{"url":"https://arxiv.org/abs/1704.05224","open_access":"1"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We compare finite rank perturbations of the following three ensembles of complex rectangular random matrices: First, a generalised Wishart ensemble with one random and two fixed correlation matrices introduced by Borodin and Péché, second, the product of two independent random matrices where one has correlated entries, and third, the case when the two random matrices become also coupled through a fixed matrix. The singular value statistics of all three ensembles is shown to be determinantal and we derive double contour integral representations for their respective kernels. Three different kernels are found in the limit of infinite matrix dimension at the origin of the spectrum. They depend on finite rank perturbations of the correlation and coupling matrices and are shown to be integrable. The first kernel (I) is found for two independent matrices from the second, and two weakly coupled matrices from the third ensemble. It generalises the Meijer G-kernel for two independent and uncorrelated matrices. The third kernel (III) is obtained for the generalised Wishart ensemble and for two strongly coupled matrices. It further generalises the perturbed Bessel kernel of Desrosiers and Forrester. Finally, kernel (II), found for the ensemble of two coupled matrices, provides an interpolation between the kernels (I) and (III), generalising previous findings of part of the authors."}],"title":"Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles","external_id":{"isi":["000456070200013"],"arxiv":["1704.05224"]},"article_processing_charge":"No","author":[{"first_name":"Gernot","last_name":"Akemann","full_name":"Akemann, Gernot"},{"last_name":"Checinski","full_name":"Checinski, Tomasz","first_name":"Tomasz"},{"full_name":"Liu, Dangzheng","last_name":"Liu","first_name":"Dangzheng","id":"2F947E34-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Eugene","full_name":"Strahov, Eugene","last_name":"Strahov"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Akemann, Gernot, et al. “Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated to Two Wishart Ensembles.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 55, no. 1, Institute of Mathematical Statistics, 2019, pp. 441–79, doi:10.1214/18-aihp888.","ieee":"G. Akemann, T. Checinski, D. Liu, and E. Strahov, “Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles,” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques, vol. 55, no. 1. Institute of Mathematical Statistics, pp. 441–479, 2019.","short":"G. Akemann, T. Checinski, D. Liu, E. Strahov, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55 (2019) 441–479.","ama":"Akemann G, Checinski T, Liu D, Strahov E. Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 2019;55(1):441-479. doi:10.1214/18-aihp888","apa":"Akemann, G., Checinski, T., Liu, D., & Strahov, E. (2019). Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Institute of Mathematical Statistics. https://doi.org/10.1214/18-aihp888","chicago":"Akemann, Gernot, Tomasz Checinski, Dangzheng Liu, and Eugene Strahov. “Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated to Two Wishart Ensembles.” Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-aihp888.","ista":"Akemann G, Checinski T, Liu D, Strahov E. 2019. Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 55(1), 441–479."},"date_created":"2020-01-30T10:36:50Z","doi":"10.1214/18-aihp888","date_published":"2019-02-01T00:00:00Z","page":"441-479","publication":"Annales de l'Institut Henri Poincaré, Probabilités et Statistiques","day":"01","year":"2019","isi":1,"oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics"},{"oa_version":"Published Version","abstract":[{"text":"We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the recent result of Ajanki et al. [‘Stability of the matrix Dyson equation and random matrices with correlations’, Probab. Theory Related Fields 173(1–2) (2019), 293–373] to allow slow correlation decay and arbitrary expectation. The main novel tool is\r\na systematic diagrammatic control of a multivariate cumulant expansion.","lang":"eng"}],"intvolume":" 7","month":"03","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"6883","checksum":"933a472568221c73b2c3ce8c87bf6d15","creator":"dernst","date_updated":"2020-07-14T12:47:22Z","file_size":1520344,"date_created":"2019-09-17T14:24:13Z","file_name":"2019_Forum_Erdoes.pdf"}],"publication_status":"published","publication_identifier":{"eissn":["20505094"]},"ec_funded":1,"volume":7,"related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"}]},"_id":"6182","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","ddc":["510"],"date_updated":"2023-09-07T12:54:12Z","file_date_updated":"2020-07-14T12:47:22Z","department":[{"_id":"LaEr"}],"oa":1,"quality_controlled":"1","publisher":"Cambridge University Press","publication":"Forum of Mathematics, Sigma","day":"26","year":"2019","isi":1,"has_accepted_license":"1","date_created":"2019-03-28T09:05:23Z","date_published":"2019-03-26T00:00:00Z","doi":"10.1017/fms.2019.2","article_number":"e8","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8.","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma. Cambridge University Press, 2019. https://doi.org/10.1017/fms.2019.2.","ama":"Erdös L, Krüger TH, Schröder DJ. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 2019;7. doi:10.1017/fms.2019.2","apa":"Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Random matrices with slow correlation decay. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2019.2","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Forum of Mathematics, Sigma 7 (2019).","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Random matrices with slow correlation decay,” Forum of Mathematics, Sigma, vol. 7. Cambridge University Press, 2019.","mla":"Erdös, László, et al. “Random Matrices with Slow Correlation Decay.” Forum of Mathematics, Sigma, vol. 7, e8, Cambridge University Press, 2019, doi:10.1017/fms.2019.2."},"title":"Random matrices with slow correlation decay","article_processing_charge":"No","external_id":{"isi":["000488847100001"],"arxiv":["1705.10661"]},"author":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}]},{"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Cipolloni, Giorgio, László Erdös, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis . MSP, 2019. https://doi.org/10.2140/paa.2019.1.615.","ista":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. 2019. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 1(4), 615–707.","mla":"Cipolloni, Giorgio, et al. “Cusp Universality for Random Matrices, II: The Real Symmetric Case.” Pure and Applied Analysis , vol. 1, no. 4, MSP, 2019, pp. 615–707, doi:10.2140/paa.2019.1.615.","ieee":"G. Cipolloni, L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices, II: The real symmetric case,” Pure and Applied Analysis , vol. 1, no. 4. MSP, pp. 615–707, 2019.","short":"G. Cipolloni, L. Erdös, T.H. Krüger, D.J. Schröder, Pure and Applied Analysis 1 (2019) 615–707.","apa":"Cipolloni, G., Erdös, L., Krüger, T. H., & Schröder, D. J. (2019). Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . MSP. https://doi.org/10.2140/paa.2019.1.615","ama":"Cipolloni G, Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices, II: The real symmetric case. Pure and Applied Analysis . 2019;1(4):615–707. doi:10.2140/paa.2019.1.615"},"title":"Cusp universality for random matrices, II: The real symmetric case","article_processing_charge":"No","external_id":{"arxiv":["1811.04055"]},"author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"International IST Doctoral Program","grant_number":"665385"}],"publication":"Pure and Applied Analysis ","day":"12","year":"2019","date_created":"2019-03-28T10:21:17Z","doi":"10.2140/paa.2019.1.615","date_published":"2019-10-12T00:00:00Z","page":"615–707","oa":1,"publisher":"MSP","quality_controlled":"1","date_updated":"2023-09-07T12:54:12Z","department":[{"_id":"LaEr"}],"_id":"6186","status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"ec_funded":1,"volume":1,"issue":"4","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"6179"}]},"oa_version":"Preprint","abstract":[{"text":"We prove that the local eigenvalue statistics of real symmetric Wigner-type\r\nmatrices near the cusp points of the eigenvalue density are universal. Together\r\nwith the companion paper [arXiv:1809.03971], which proves the same result for\r\nthe complex Hermitian symmetry class, this completes the last remaining case of\r\nthe Wigner-Dyson-Mehta universality conjecture after bulk and edge\r\nuniversalities have been established in the last years. We extend the recent\r\nDyson Brownian motion analysis at the edge [arXiv:1712.03881] to the cusp\r\nregime using the optimal local law from [arXiv:1809.03971] and the accurate\r\nlocal shape analysis of the density from [arXiv:1506.05095, arXiv:1804.07752].\r\nWe also present a PDE-based method to improve the estimate on eigenvalue\r\nrigidity via the maximum principle of the heat flow related to the Dyson\r\nBrownian motion.","lang":"eng"}],"intvolume":" 1","month":"10","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.04055"}]},{"status":"public","keyword":["Random Schrödinger operators","spectral shift function","Anderson orthogonality"],"type":"journal_article","article_type":"original","_id":"10879","department":[{"_id":"LaEr"}],"date_updated":"2023-09-08T11:35:31Z","month":"03","intvolume":" 9","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1701.02956","open_access":"1"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We study effects of a bounded and compactly supported perturbation on multidimensional continuum random Schrödinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schrödinger operators. Among others, we prove that Anderson orthogonality does occur for Fermi energies in the region of complete localisation with a non-zero probability. This partially confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11 (2015), 560–565]. The spectral shift function plays an important role in our analysis of Anderson orthogonality. We identify it with the index of the corresponding pair of spectral projections and explore the consequences thereof. All our results rely on the main technical estimate of this paper which guarantees separate exponential decay of the disorder-averaged Schatten p-norm of χa(f(H)−f(Hτ))χb in a and b. Here, Hτ is a perturbation of the random Schrödinger operator H, χa is the multiplication operator corresponding to the indicator function of a unit cube centred about a∈Rd, and f is in a suitable class of functions of bounded variation with distributional derivative supported in the region of complete localisation for H."}],"issue":"3","volume":9,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["1664-039X"]},"publication_status":"published","title":"Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function","author":[{"last_name":"Dietlein","full_name":"Dietlein, Adrian M","id":"317CB464-F248-11E8-B48F-1D18A9856A87","first_name":"Adrian M"},{"first_name":"Martin","full_name":"Gebert, Martin","last_name":"Gebert"},{"last_name":"Müller","full_name":"Müller, Peter","first_name":"Peter"}],"article_processing_charge":"No","external_id":{"isi":["000484709400006"],"arxiv":["1701.02956"]},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"chicago":"Dietlein, Adrian M, Martin Gebert, and Peter Müller. “Perturbations of Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.” Journal of Spectral Theory. European Mathematical Society Publishing House, 2019. https://doi.org/10.4171/jst/267.","ista":"Dietlein AM, Gebert M, Müller P. 2019. Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. 9(3), 921–965.","mla":"Dietlein, Adrian M., et al. “Perturbations of Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.” Journal of Spectral Theory, vol. 9, no. 3, European Mathematical Society Publishing House, 2019, pp. 921–65, doi:10.4171/jst/267.","ieee":"A. M. Dietlein, M. Gebert, and P. Müller, “Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function,” Journal of Spectral Theory, vol. 9, no. 3. European Mathematical Society Publishing House, pp. 921–965, 2019.","short":"A.M. Dietlein, M. Gebert, P. Müller, Journal of Spectral Theory 9 (2019) 921–965.","ama":"Dietlein AM, Gebert M, Müller P. Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. 2019;9(3):921-965. doi:10.4171/jst/267","apa":"Dietlein, A. M., Gebert, M., & Müller, P. (2019). Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. European Mathematical Society Publishing House. https://doi.org/10.4171/jst/267"},"publisher":"European Mathematical Society Publishing House","quality_controlled":"1","oa":1,"acknowledgement":"M.G. was supported by the DFG under grant GE 2871/1-1.","date_published":"2019-03-01T00:00:00Z","doi":"10.4171/jst/267","date_created":"2022-03-18T12:36:42Z","page":"921-965","day":"01","publication":"Journal of Spectral Theory","isi":1,"year":"2019"},{"oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","day":"25","year":"2019","isi":1,"date_created":"2018-12-11T11:44:29Z","doi":"10.1214/18-AIHP916","date_published":"2019-09-25T00:00:00Z","page":"1203-1225","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 55(3), 1203–1225.","chicago":"Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2019. https://doi.org/10.1214/18-AIHP916.","apa":"Ferrari, P., Ghosal, P., & Nejjar, P. (2019). Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/18-AIHP916","ama":"Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2019;55(3):1203-1225. doi:10.1214/18-AIHP916","ieee":"P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle in TASEP with non-random initial condition,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 3. Institute of Mathematical Statistics, pp. 1203–1225, 2019.","short":"P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.","mla":"Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 55, no. 3, Institute of Mathematical Statistics, 2019, pp. 1203–25, doi:10.1214/18-AIHP916."},"title":"Limit law of a second class particle in TASEP with non-random initial condition","external_id":{"arxiv":["1710.02323"],"isi":["000487763200001"]},"article_processing_charge":"No","author":[{"full_name":"Ferrari, Patrick","last_name":"Ferrari","first_name":"Patrick"},{"first_name":"Promit","last_name":"Ghosal","full_name":"Ghosal, Promit"},{"first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","last_name":"Nejjar","full_name":"Nejjar, Peter"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle initially at the origin. For ρ<λ, there is a shock and the second class particle moves with speed 1−λ−ρ. For large time t, we show that the position of the second class particle fluctuates on a t1/3 scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time t."}],"intvolume":" 55","month":"09","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1710.02323"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0246-0203"]},"ec_funded":1,"volume":55,"issue":"3","_id":"72","status":"public","type":"journal_article","article_type":"original","date_updated":"2023-10-17T08:53:45Z","department":[{"_id":"LaEr"},{"_id":"JaMa"}]},{"page":"661-696","date_created":"2019-04-08T14:05:04Z","doi":"10.1214/18-AIHP894","date_published":"2019-05-01T00:00:00Z","year":"2019","isi":1,"publication":"Annales de l'institut Henri Poincare","day":"01","oa":1,"publisher":"Institut Henri Poincaré","quality_controlled":"1","external_id":{"arxiv":["1706.08343"],"isi":["000467793600003"]},"article_processing_charge":"No","author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes","last_name":"Alt","full_name":"Alt, Johannes"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H"},{"last_name":"Nemish","full_name":"Nemish, Yuriy","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy"}],"title":"Location of the spectrum of Kronecker random matrices","citation":{"ista":"Alt J, Erdös L, Krüger TH, Nemish Y. 2019. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 55(2), 661–696.","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Yuriy Nemish. “Location of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri Poincare. Institut Henri Poincaré, 2019. https://doi.org/10.1214/18-AIHP894.","ieee":"J. Alt, L. Erdös, T. H. Krüger, and Y. Nemish, “Location of the spectrum of Kronecker random matrices,” Annales de l’institut Henri Poincare, vol. 55, no. 2. Institut Henri Poincaré, pp. 661–696, 2019.","short":"J. Alt, L. Erdös, T.H. Krüger, Y. Nemish, Annales de l’institut Henri Poincare 55 (2019) 661–696.","apa":"Alt, J., Erdös, L., Krüger, T. H., & Nemish, Y. (2019). Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. Institut Henri Poincaré. https://doi.org/10.1214/18-AIHP894","ama":"Alt J, Erdös L, Krüger TH, Nemish Y. Location of the spectrum of Kronecker random matrices. Annales de l’institut Henri Poincare. 2019;55(2):661-696. doi:10.1214/18-AIHP894","mla":"Alt, Johannes, et al. “Location of the Spectrum of Kronecker Random Matrices.” Annales de l’institut Henri Poincare, vol. 55, no. 2, Institut Henri Poincaré, 2019, pp. 661–96, doi:10.1214/18-AIHP894."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"ec_funded":1,"issue":"2","volume":55,"related_material":{"record":[{"id":"149","status":"public","relation":"dissertation_contains"}]},"publication_status":"published","publication_identifier":{"issn":["0246-0203"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1706.08343","open_access":"1"}],"scopus_import":"1","intvolume":" 55","month":"05","abstract":[{"lang":"eng","text":"For a general class of large non-Hermitian random block matrices X we prove that there are no eigenvalues away from a deterministic set with very high probability. This set is obtained from the Dyson equation of the Hermitization of X as the self-consistent approximation of the pseudospectrum. We demonstrate that the analysis of the matrix Dyson equation from (Probab. Theory Related Fields (2018)) offers a unified treatment of many structured matrix ensembles."}],"oa_version":"Preprint","department":[{"_id":"LaEr"}],"date_updated":"2023-10-17T12:20:20Z","type":"journal_article","status":"public","_id":"6240"},{"alternative_title":["ISTA Thesis"],"month":"03","abstract":[{"lang":"eng","text":"In the first part of this thesis we consider large random matrices with arbitrary expectation and a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent in the bulk and edge regime. The main novel tool is a systematic diagrammatic control of a multivariate cumulant expansion.\r\nIn the second part we consider Wigner-type matrices and show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are uni- versal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner- Dyson-Mehta universality conjecture for the last remaining universality type. Our analysis holds not only for exact cusps, but approximate cusps as well, where an ex- tended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp, and extend the fast relaxation to equilibrium of the Dyson Brow- nian motion to the cusp regime.\r\nIn the third and final part we explore the entrywise linear statistics of Wigner ma- trices and identify the fluctuations for a large class of test functions with little regularity. This enables us to study the rectangular Young diagram obtained from the interlacing eigenvalues of the random matrix and its minor, and we find that, despite having the same limit, the fluctuations differ from those of the algebraic Young tableaux equipped with the Plancharel measure."}],"oa_version":"Published Version","ec_funded":1,"related_material":{"record":[{"relation":"part_of_dissertation","id":"1144","status":"public"},{"id":"6186","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","id":"6185","status":"public"},{"id":"6182","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"1012"},{"relation":"part_of_dissertation","status":"public","id":"6184"}]},"degree_awarded":"PhD","publication_status":"published","publication_identifier":{"issn":["2663-337X"]},"language":[{"iso":"eng"}],"file":[{"checksum":"6926f66f28079a81c4937e3764be00fc","file_id":"6180","content_type":"application/x-gzip","relation":"source_file","access_level":"closed","file_name":"2019_Schroeder_Thesis.tar.gz","date_created":"2019-03-28T08:53:52Z","file_size":7104482,"date_updated":"2020-07-14T12:47:21Z","creator":"dernst"},{"date_created":"2019-03-28T08:53:52Z","file_name":"2019_Schroeder_Thesis.pdf","date_updated":"2020-07-14T12:47:21Z","file_size":4228794,"creator":"dernst","checksum":"7d0ebb8d1207e89768cdd497a5bf80fb","file_id":"6181","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"type":"dissertation","status":"public","_id":"6179","department":[{"_id":"LaEr"}],"file_date_updated":"2020-07-14T12:47:21Z","date_updated":"2024-02-22T14:34:33Z","supervisor":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"}],"ddc":["515","519"],"oa":1,"publisher":"Institute of Science and Technology Austria","page":"375","date_created":"2019-03-28T08:58:59Z","date_published":"2019-03-18T00:00:00Z","doi":"10.15479/AT:ISTA:th6179","year":"2019","has_accepted_license":"1","day":"18","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"article_processing_charge":"No","author":[{"last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"title":"From Dyson to Pearcey: Universal statistics in random matrix theory","citation":{"chicago":"Schröder, Dominik J. “From Dyson to Pearcey: Universal Statistics in Random Matrix Theory.” Institute of Science and Technology Austria, 2019. https://doi.org/10.15479/AT:ISTA:th6179.","ista":"Schröder DJ. 2019. From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria.","mla":"Schröder, Dominik J. From Dyson to Pearcey: Universal Statistics in Random Matrix Theory. Institute of Science and Technology Austria, 2019, doi:10.15479/AT:ISTA:th6179.","ieee":"D. J. Schröder, “From Dyson to Pearcey: Universal statistics in random matrix theory,” Institute of Science and Technology Austria, 2019.","short":"D.J. Schröder, From Dyson to Pearcey: Universal Statistics in Random Matrix Theory, Institute of Science and Technology Austria, 2019.","apa":"Schröder, D. J. (2019). From Dyson to Pearcey: Universal statistics in random matrix theory. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:th6179","ama":"Schröder DJ. From Dyson to Pearcey: Universal statistics in random matrix theory. 2019. doi:10.15479/AT:ISTA:th6179"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1"},{"date_created":"2018-12-11T11:47:56Z","date_published":"2018-06-14T00:00:00Z","doi":"10.1007/s00440-017-0787-8","publication":"Probability Theory and Related Fields","day":"14","year":"2018","oa":1,"quality_controlled":"1","publisher":"Springer","title":"Local law and Tracy–Widom limit for sparse random matrices","external_id":{"arxiv":["1605.08767"]},"author":[{"last_name":"Lee","full_name":"Lee, Jii","first_name":"Jii"},{"orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"}],"publist_id":"7017","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random Matrices.” Probability Theory and Related Fields, vol. 171, no. 1–2, 543–616, Springer, 2018, doi:10.1007/s00440-017-0787-8.","apa":"Lee, J., & Schnelli, K. (2018). Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-017-0787-8","ama":"Lee J, Schnelli K. Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. 2018;171(1-2). doi:10.1007/s00440-017-0787-8","ieee":"J. Lee and K. Schnelli, “Local law and Tracy–Widom limit for sparse random matrices,” Probability Theory and Related Fields, vol. 171, no. 1–2. Springer, 2018.","short":"J. Lee, K. Schnelli, Probability Theory and Related Fields 171 (2018).","chicago":"Lee, Jii, and Kevin Schnelli. “Local Law and Tracy–Widom Limit for Sparse Random Matrices.” Probability Theory and Related Fields. Springer, 2018. https://doi.org/10.1007/s00440-017-0787-8.","ista":"Lee J, Schnelli K. 2018. Local law and Tracy–Widom limit for sparse random matrices. Probability Theory and Related Fields. 171(1–2), 543–616."},"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"article_number":"543-616","ec_funded":1,"volume":171,"issue":"1-2","language":[{"iso":"eng"}],"publication_status":"published","intvolume":" 171","month":"06","main_file_link":[{"url":"https://arxiv.org/abs/1605.08767","open_access":"1"}],"scopus_import":1,"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider spectral properties and the edge universality of sparse random matrices, the class of random matrices that includes the adjacency matrices of the Erdős–Rényi graph model G(N, p). We prove a local law for the eigenvalue density up to the spectral edges. Under a suitable condition on the sparsity, we also prove that the rescaled extremal eigenvalues exhibit GOE Tracy–Widom fluctuations if a deterministic shift of the spectral edge due to the sparsity is included. For the adjacency matrix of the Erdős–Rényi graph this establishes the Tracy–Widom fluctuations of the second largest eigenvalue when p is much larger than N−2/3 with a deterministic shift of order (Np)−1."}],"department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T08:09:33Z","status":"public","type":"journal_article","_id":"690"},{"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"isi":1,"year":"2018","day":"03","publication":"Annals Applied Probability ","page":"148-203","doi":"10.1214/17-AAP1302","date_published":"2018-03-03T00:00:00Z","date_created":"2018-12-11T11:47:13Z","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"citation":{"chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Local Inhomogeneous Circular Law.” Annals Applied Probability . Institute of Mathematical Statistics, 2018. https://doi.org/10.1214/17-AAP1302.","ista":"Alt J, Erdös L, Krüger TH. 2018. Local inhomogeneous circular law. Annals Applied Probability . 28(1), 148–203.","mla":"Alt, Johannes, et al. “Local Inhomogeneous Circular Law.” Annals Applied Probability , vol. 28, no. 1, Institute of Mathematical Statistics, 2018, pp. 148–203, doi:10.1214/17-AAP1302.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Local inhomogeneous circular law,” Annals Applied Probability , vol. 28, no. 1. Institute of Mathematical Statistics, pp. 148–203, 2018.","short":"J. Alt, L. Erdös, T.H. Krüger, Annals Applied Probability 28 (2018) 148–203.","ama":"Alt J, Erdös L, Krüger TH. Local inhomogeneous circular law. Annals Applied Probability . 2018;28(1):148-203. doi:10.1214/17-AAP1302","apa":"Alt, J., Erdös, L., & Krüger, T. H. (2018). Local inhomogeneous circular law. Annals Applied Probability . Institute of Mathematical Statistics. https://doi.org/10.1214/17-AAP1302"},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","author":[{"first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","full_name":"Alt, Johannes"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger"}],"external_id":{"isi":["000431721800005"],"arxiv":["1612.07776 "]},"article_processing_charge":"No","title":"Local inhomogeneous circular law","abstract":[{"lang":"eng","text":"We consider large random matrices X with centered, independent entries which have comparable but not necessarily identical variances. Girko's circular law asserts that the spectrum is supported in a disk and in case of identical variances, the limiting density is uniform. In this special case, the local circular law by Bourgade et. al. [11,12] shows that the empirical density converges even locally on scales slightly above the typical eigenvalue spacing. In the general case, the limiting density is typically inhomogeneous and it is obtained via solving a system of deterministic equations. Our main result is the local inhomogeneous circular law in the bulk spectrum on the optimal scale for a general variance profile of the entries of X. \r\n\r\n"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1612.07776 "}],"month":"03","intvolume":" 28","publication_status":"published","language":[{"iso":"eng"}],"related_material":{"record":[{"id":"149","status":"public","relation":"dissertation_contains"}]},"issue":"1","volume":28,"ec_funded":1,"_id":"566","article_type":"original","type":"journal_article","status":"public","date_updated":"2023-09-13T08:47:52Z","department":[{"_id":"LaEr"}]},{"language":[{"iso":"eng"}],"publication_status":"published","ec_funded":1,"issue":"3","volume":50,"oa_version":"Published Version","abstract":[{"text":"We consider large random matrices X with centered, independent entries but possibly di erent variances. We compute the normalized trace of f(X)g(X∗) for f, g functions analytic on the spectrum of X. We use these results to compute the long time asymptotics for systems of coupled di erential equations with random coe cients. We show that when the coupling is critical, the norm squared of the solution decays like t−1/2.","lang":"eng"}],"intvolume":" 50","month":"01","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01546"}],"scopus_import":"1","date_updated":"2023-09-15T12:05:52Z","department":[{"_id":"LaEr"}],"_id":"181","status":"public","type":"journal_article","publication":"SIAM Journal on Mathematical Analysis","day":"01","year":"2018","isi":1,"date_created":"2018-12-11T11:45:03Z","doi":"10.1137/17M1143125","date_published":"2018-01-01T00:00:00Z","page":"3271 - 3290","acknowledgement":"The work of the second author was also partially supported by the Hausdorff Center of Mathematics.","oa":1,"quality_controlled":"1","publisher":"Society for Industrial and Applied Mathematics ","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"ista":"Erdös L, Krüger TH, Renfrew DT. 2018. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 50(3), 3271–3290.","chicago":"Erdös, László, Torben H Krüger, and David T Renfrew. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics , 2018. https://doi.org/10.1137/17M1143125.","short":"L. Erdös, T.H. Krüger, D.T. Renfrew, SIAM Journal on Mathematical Analysis 50 (2018) 3271–3290.","ieee":"L. Erdös, T. H. Krüger, and D. T. Renfrew, “Power law decay for systems of randomly coupled differential equations,” SIAM Journal on Mathematical Analysis, vol. 50, no. 3. Society for Industrial and Applied Mathematics , pp. 3271–3290, 2018.","ama":"Erdös L, Krüger TH, Renfrew DT. Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. 2018;50(3):3271-3290. doi:10.1137/17M1143125","apa":"Erdös, L., Krüger, T. H., & Renfrew, D. T. (2018). Power law decay for systems of randomly coupled differential equations. SIAM Journal on Mathematical Analysis. Society for Industrial and Applied Mathematics . https://doi.org/10.1137/17M1143125","mla":"Erdös, László, et al. “Power Law Decay for Systems of Randomly Coupled Differential Equations.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society for Industrial and Applied Mathematics , 2018, pp. 3271–90, doi:10.1137/17M1143125."},"title":"Power law decay for systems of randomly coupled differential equations","article_processing_charge":"No","external_id":{"isi":["000437018500032"],"arxiv":["1708.01546"]},"author":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"last_name":"Krüger","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"first_name":"David T","id":"4845BF6A-F248-11E8-B48F-1D18A9856A87","full_name":"Renfrew, David T","orcid":"0000-0003-3493-121X","last_name":"Renfrew"}],"publist_id":"7740","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"258F40A4-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","grant_number":"M02080","name":"Structured Non-Hermitian Random Matrices"}]},{"publication_status":"published","publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"language":[{"iso":"eng"}],"ec_funded":1,"abstract":[{"text":"We consider a Wigner-type ensemble, i.e. large hermitian N×N random matrices H=H∗ with centered independent entries and with a general matrix of variances Sxy=𝔼∣∣Hxy∣∣2. The norm of H is asymptotically given by the maximum of the support of the self-consistent density of states. We establish a bound on this maximum in terms of norms of powers of S that substantially improves the earlier bound 2∥S∥1/2∞ given in [O. Ajanki, L. Erdős and T. Krüger, Universality for general Wigner-type matrices, Prob. Theor. Rel. Fields169 (2017) 667–727]. The key element of the proof is an effective Markov chain approximation for the contributions of the weighted Dyck paths appearing in the iterative solution of the corresponding Dyson equation.","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"url":"https://arxiv.org/abs/1802.05175","open_access":"1"}],"scopus_import":"1","month":"09","date_updated":"2023-09-19T14:24:05Z","department":[{"_id":"LaEr"}],"_id":"5971","type":"journal_article","status":"public","year":"2018","isi":1,"publication":"Random matrices: Theory and applications","day":"26","date_created":"2019-02-13T10:40:54Z","date_published":"2018-09-26T00:00:00Z","doi":"10.1142/s2010326319500096","oa":1,"quality_controlled":"1","publisher":"World Scientific Publishing","citation":{"ista":"Erdös L, Mühlbacher P. 2018. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications., 1950009.","chicago":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications. World Scientific Publishing, 2018. https://doi.org/10.1142/s2010326319500096.","ieee":"L. Erdös and P. Mühlbacher, “Bounds on the norm of Wigner-type random matrices,” Random matrices: Theory and applications. World Scientific Publishing, 2018.","short":"L. Erdös, P. Mühlbacher, Random Matrices: Theory and Applications (2018).","apa":"Erdös, L., & Mühlbacher, P. (2018). Bounds on the norm of Wigner-type random matrices. Random Matrices: Theory and Applications. World Scientific Publishing. https://doi.org/10.1142/s2010326319500096","ama":"Erdös L, Mühlbacher P. Bounds on the norm of Wigner-type random matrices. Random matrices: Theory and applications. 2018. doi:10.1142/s2010326319500096","mla":"Erdös, László, and Peter Mühlbacher. “Bounds on the Norm of Wigner-Type Random Matrices.” Random Matrices: Theory and Applications, 1950009, World Scientific Publishing, 2018, doi:10.1142/s2010326319500096."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"isi":["000477677200002"],"arxiv":["1802.05175"]},"article_processing_charge":"No","author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"first_name":"Peter","full_name":"Mühlbacher, Peter","last_name":"Mühlbacher"}],"title":"Bounds on the norm of Wigner-type random matrices","article_number":"1950009","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}]},{"volume":2018,"issue":"10","related_material":{"record":[{"id":"6179","status":"public","relation":"dissertation_contains"}]},"ec_funded":1,"publication_identifier":{"issn":["10737928"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1608.05163"}],"month":"05","intvolume":" 2018","abstract":[{"text":"We prove a new central limit theorem (CLT) for the difference of linear eigenvalue statistics of a Wigner random matrix H and its minor H and find that the fluctuation is much smaller than the fluctuations of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of H and H. In particular, our theorem identifies the fluctuation of Kerov's rectangular Young diagrams, defined by the interlacing eigenvalues ofH and H, around their asymptotic shape, the Vershik'Kerov'Logan'Shepp curve. Young diagrams equipped with the Plancherel measure follow the same limiting shape. For this, algebraically motivated, ensemble a CLT has been obtained in Ivanov and Olshanski [20] which is structurally similar to our result but the variance is different, indicating that the analogy between the two models has its limitations. Moreover, our theorem shows that Borodin's result [7] on the convergence of the spectral distribution of Wigner matrices to a Gaussian free field also holds in derivative sense.","lang":"eng"}],"oa_version":"Preprint","department":[{"_id":"LaEr"}],"date_updated":"2023-09-22T09:44:21Z","type":"journal_article","status":"public","_id":"1012","page":"3255-3298","date_published":"2018-05-18T00:00:00Z","doi":"10.1093/imrn/rnw330","date_created":"2018-12-11T11:49:41Z","isi":1,"year":"2018","day":"18","publication":"International Mathematics Research Notices","publisher":"Oxford University Press","quality_controlled":"1","oa":1,"publist_id":"6383","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"external_id":{"arxiv":["1608.05163"],"isi":["000441668300009"]},"article_processing_charge":"No","title":"Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues","citation":{"ista":"Erdös L, Schröder DJ. 2018. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018(10), 3255–3298.","chicago":"Erdös, László, and Dominik J Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices. Oxford University Press, 2018. https://doi.org/10.1093/imrn/rnw330.","ama":"Erdös L, Schröder DJ. Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. 2018;2018(10):3255-3298. doi:10.1093/imrn/rnw330","apa":"Erdös, L., & Schröder, D. J. (2018). Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues. International Mathematics Research Notices. Oxford University Press. https://doi.org/10.1093/imrn/rnw330","ieee":"L. Erdös and D. J. Schröder, “Fluctuations of rectangular young diagrams of interlacing wigner eigenvalues,” International Mathematics Research Notices, vol. 2018, no. 10. Oxford University Press, pp. 3255–3298, 2018.","short":"L. Erdös, D.J. Schröder, International Mathematics Research Notices 2018 (2018) 3255–3298.","mla":"Erdös, László, and Dominik J. Schröder. “Fluctuations of Rectangular Young Diagrams of Interlacing Wigner Eigenvalues.” International Mathematics Research Notices, vol. 2018, no. 10, Oxford University Press, 2018, pp. 3255–98, doi:10.1093/imrn/rnw330."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}]},{"status":"public","article_type":"original","type":"journal_article","_id":"70","file_date_updated":"2020-07-14T12:47:46Z","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"ddc":["510"],"date_updated":"2023-10-10T13:11:29Z","intvolume":" 15","month":"10","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"We consider the totally asymmetric simple exclusion process in a critical scaling parametrized by a≥0, which creates a shock in the particle density of order aT−1/3, T the observation time. When starting from step initial data, we provide bounds on the limiting law which in particular imply that in the double limit lima→∞limT→∞ one recovers the product limit law and the degeneration of the correlation length observed at shocks of order 1. This result is shown to apply to a general last-passage percolation model. We also obtain bounds on the two-point functions of several airy processes.","lang":"eng"}],"ec_funded":1,"issue":"2","volume":15,"language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"5981","checksum":"2ded46aa284a836a8cbb34133a64f1cb","creator":"kschuh","file_size":394851,"date_updated":"2020-07-14T12:47:46Z","file_name":"2018_ALEA_Nejjar.pdf","date_created":"2019-02-14T09:44:10Z"}],"publication_status":"published","publication_identifier":{"issn":["1980-0436"]},"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117"}],"title":"Transition to shocks in TASEP and decoupling of last passage times","article_processing_charge":"No","external_id":{"arxiv":["1705.08836"],"isi":["000460475800022"]},"author":[{"first_name":"Peter","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","last_name":"Nejjar","full_name":"Nejjar, Peter"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2, Instituto Nacional de Matematica Pura e Aplicada, 2018, pp. 1311–34, doi:10.30757/ALEA.v15-49.","short":"P. Nejjar, Latin American Journal of Probability and Mathematical Statistics 15 (2018) 1311–1334.","ieee":"P. Nejjar, “Transition to shocks in TASEP and decoupling of last passage times,” Latin American Journal of Probability and Mathematical Statistics, vol. 15, no. 2. Instituto Nacional de Matematica Pura e Aplicada, pp. 1311–1334, 2018.","apa":"Nejjar, P. (2018). Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v15-49","ama":"Nejjar P. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 2018;15(2):1311-1334. doi:10.30757/ALEA.v15-49","chicago":"Nejjar, Peter. “Transition to Shocks in TASEP and Decoupling of Last Passage Times.” Latin American Journal of Probability and Mathematical Statistics. Instituto Nacional de Matematica Pura e Aplicada, 2018. https://doi.org/10.30757/ALEA.v15-49.","ista":"Nejjar P. 2018. Transition to shocks in TASEP and decoupling of last passage times. Latin American Journal of Probability and Mathematical Statistics. 15(2), 1311–1334."},"oa":1,"quality_controlled":"1","publisher":"Instituto Nacional de Matematica Pura e Aplicada","date_created":"2018-12-11T11:44:28Z","date_published":"2018-10-01T00:00:00Z","doi":"10.30757/ALEA.v15-49","page":"1311-1334","publication":"Latin American Journal of Probability and Mathematical Statistics","day":"01","year":"2018","has_accepted_license":"1","isi":1},{"publication_identifier":{"issn":["0001-6969"],"eissn":["2064-8316"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"1-2","volume":84,"ec_funded":1,"abstract":[{"text":"Borel probability measures living on metric spaces are fundamental\r\nmathematical objects. There are several meaningful distance functions that make the collection of the probability measures living on a certain space a metric space. We are interested in the description of the structure of the isometries of such metric spaces. We overview some of the recent results of the topic and we also provide some new ones concerning the Wasserstein distance. More specifically, we consider the space of all Borel probability measures on the unit sphere of a Euclidean space endowed with the Wasserstein metric W_p for arbitrary p >= 1, and we show that the action of a Wasserstein isometry on the set of Dirac measures is induced by an isometry of the underlying unit sphere.","lang":"eng"}],"oa_version":"Preprint","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1802.03305"}],"month":"06","intvolume":" 84","date_updated":"2023-10-16T10:29:22Z","department":[{"_id":"LaEr"}],"_id":"284","type":"journal_article","article_type":"original","status":"public","year":"2018","day":"04","publication":"Acta Scientiarum Mathematicarum","page":"65 - 80","date_published":"2018-06-04T00:00:00Z","doi":"10.14232/actasm-018-753-y","date_created":"2018-12-11T11:45:36Z","acknowledgement":"The author was supported by the ISTFELLOW program of the Institute of Science and Technol- ogy Austria (project code IC1027FELL01) and partially supported by the Hungarian National Research, Development and Innovation Office, NKFIH (grant no. K124152).","publisher":"Springer Nature","quality_controlled":"1","oa":1,"citation":{"mla":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” Acta Scientiarum Mathematicarum, vol. 84, no. 1–2, Springer Nature, 2018, pp. 65–80, doi:10.14232/actasm-018-753-y.","ieee":"D. Virosztek, “Maps on probability measures preserving certain distances - a survey and some new results,” Acta Scientiarum Mathematicarum, vol. 84, no. 1–2. Springer Nature, pp. 65–80, 2018.","short":"D. Virosztek, Acta Scientiarum Mathematicarum 84 (2018) 65–80.","ama":"Virosztek D. Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. 2018;84(1-2):65-80. doi:10.14232/actasm-018-753-y","apa":"Virosztek, D. (2018). Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. Springer Nature. https://doi.org/10.14232/actasm-018-753-y","chicago":"Virosztek, Daniel. “Maps on Probability Measures Preserving Certain Distances - a Survey and Some New Results.” Acta Scientiarum Mathematicarum. Springer Nature, 2018. https://doi.org/10.14232/actasm-018-753-y.","ista":"Virosztek D. 2018. Maps on probability measures preserving certain distances - a survey and some new results. Acta Scientiarum Mathematicarum. 84(1–2), 65–80."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"7615","author":[{"last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"arxiv":["1802.03305"]},"title":"Maps on probability measures preserving certain distances - a survey and some new results","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"291734","name":"International IST Postdoc Fellowship Programme"}]},{"month":"04","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.07752"}],"oa":1,"oa_version":"Preprint","abstract":[{"text":"We study the unique solution $m$ of the Dyson equation \\[ -m(z)^{-1} = z - a\r\n+ S[m(z)] \\] on a von Neumann algebra $\\mathcal{A}$ with the constraint\r\n$\\mathrm{Im}\\,m\\geq 0$. Here, $z$ lies in the complex upper half-plane, $a$ is\r\na self-adjoint element of $\\mathcal{A}$ and $S$ is a positivity-preserving\r\nlinear operator on $\\mathcal{A}$. We show that $m$ is the Stieltjes transform\r\nof a compactly supported $\\mathcal{A}$-valued measure on $\\mathbb{R}$. Under\r\nsuitable assumptions, we establish that this measure has a uniformly\r\n$1/3$-H\\\"{o}lder continuous density with respect to the Lebesgue measure, which\r\nis supported on finitely many intervals, called bands. In fact, the density is\r\nanalytic inside the bands with a square-root growth at the edges and internal\r\ncubic root cusps whenever the gap between two bands vanishes. The shape of\r\nthese singularities is universal and no other singularity may occur. We give a\r\nprecise asymptotic description of $m$ near the singular points. These\r\nasymptotics generalize the analysis at the regular edges given in the companion\r\npaper on the Tracy-Widom universality for the edge eigenvalue statistics for\r\ncorrelated random matrices [arXiv:1804.07744] and they play a key role in the\r\nproof of the Pearcey universality at the cusp for Wigner-type matrices\r\n[arXiv:1809.03971,arXiv:1811.04055]. We also extend the finite dimensional band\r\nmass formula from [arXiv:1804.07744] to the von Neumann algebra setting by\r\nshowing that the spectral mass of the bands is topologically rigid under\r\ndeformations and we conclude that these masses are quantized in some important\r\ncases.","lang":"eng"}],"date_published":"2018-04-20T00:00:00Z","related_material":{"record":[{"status":"public","id":"149","relation":"dissertation_contains"},{"status":"public","id":"14694","relation":"later_version"}]},"date_created":"2019-03-28T09:20:06Z","day":"20","language":[{"iso":"eng"}],"publication":"arXiv","year":"2018","publication_status":"submitted","status":"public","type":"preprint","article_number":"1804.07752","_id":"6183","department":[{"_id":"LaEr"}],"title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","author":[{"full_name":"Alt, Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H"}],"external_id":{"arxiv":["1804.07752"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” ArXiv, n.d.","ista":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. arXiv, 1804.07752.","mla":"Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” ArXiv, 1804.07752.","short":"J. Alt, L. Erdös, T.H. Krüger, ArXiv (n.d.).","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” arXiv. .","apa":"Alt, J., Erdös, L., & Krüger, T. H. (n.d.). The Dyson equation with linear self-energy: Spectral bands, edges and cusps. arXiv.","ama":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. arXiv."},"date_updated":"2023-12-18T10:46:08Z"},{"oa":1,"publisher":"Springer Nature","quality_controlled":"1","year":"2018","has_accepted_license":"1","publication":"Annales Henri Poincare","day":"13","page":"3663-3742","date_created":"2018-12-11T11:47:09Z","doi":"10.1007/s00023-018-0723-1","date_published":"2018-11-13T00:00:00Z","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"name":"Optimal Transport and Stochastic Dynamics","grant_number":"716117","_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"ista":"Betea D, Bouttier J, Nejjar P, Vuletic M. 2018. The free boundary Schur process and applications I. Annales Henri Poincare. 19(12), 3663–3742.","chicago":"Betea, Dan, Jeremie Bouttier, Peter Nejjar, and Mirjana Vuletic. “The Free Boundary Schur Process and Applications I.” Annales Henri Poincare. Springer Nature, 2018. https://doi.org/10.1007/s00023-018-0723-1.","ama":"Betea D, Bouttier J, Nejjar P, Vuletic M. The free boundary Schur process and applications I. Annales Henri Poincare. 2018;19(12):3663-3742. doi:10.1007/s00023-018-0723-1","apa":"Betea, D., Bouttier, J., Nejjar, P., & Vuletic, M. (2018). The free boundary Schur process and applications I. Annales Henri Poincare. Springer Nature. https://doi.org/10.1007/s00023-018-0723-1","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletic, “The free boundary Schur process and applications I,” Annales Henri Poincare, vol. 19, no. 12. Springer Nature, pp. 3663–3742, 2018.","short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletic, Annales Henri Poincare 19 (2018) 3663–3742.","mla":"Betea, Dan, et al. “The Free Boundary Schur Process and Applications I.” Annales Henri Poincare, vol. 19, no. 12, Springer Nature, 2018, pp. 3663–742, doi:10.1007/s00023-018-0723-1."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["1704.05809"]},"article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Betea, Dan","last_name":"Betea","first_name":"Dan"},{"first_name":"Jeremie","last_name":"Bouttier","full_name":"Bouttier, Jeremie"},{"full_name":"Nejjar, Peter","last_name":"Nejjar","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter"},{"full_name":"Vuletic, Mirjana","last_name":"Vuletic","first_name":"Mirjana"}],"publist_id":"7258","title":"The free boundary Schur process and applications I","abstract":[{"text":"We investigate the free boundary Schur process, a variant of the Schur process introduced by Okounkov and Reshetikhin, where we allow the first and the last partitions to be arbitrary (instead of empty in the original setting). The pfaffian Schur process, previously studied by several authors, is recovered when just one of the boundary partitions is left free. We compute the correlation functions of the process in all generality via the free fermion formalism, which we extend with the thorough treatment of “free boundary states.” For the case of one free boundary, our approach yields a new proof that the process is pfaffian. For the case of two free boundaries, we find that the process is not pfaffian, but a closely related process is. We also study three different applications of the Schur process with one free boundary: fluctuations of symmetrized last passage percolation models, limit shapes and processes for symmetric plane partitions and for plane overpartitions.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 19","month":"11","publication_status":"published","publication_identifier":{"issn":["1424-0637"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"5866","checksum":"0c38abe73569b7166b7487ad5d23cc68","file_size":3084674,"date_updated":"2020-07-14T12:47:03Z","creator":"dernst","file_name":"2018_Annales_Betea.pdf","date_created":"2019-01-21T15:18:55Z"}],"ec_funded":1,"volume":19,"issue":"12","_id":"556","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","status":"public","date_updated":"2024-02-20T10:48:17Z","ddc":["500"],"file_date_updated":"2020-07-14T12:47:03Z","department":[{"_id":"LaEr"},{"_id":"JaMa"}]},{"pubrep_id":"1040","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"dissertation","_id":"149","file_date_updated":"2020-07-14T12:44:57Z","department":[{"_id":"LaEr"}],"ddc":["515","519"],"date_updated":"2024-02-22T14:34:33Z","supervisor":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"}],"month":"07","alternative_title":["ISTA Thesis"],"oa_version":"Published Version","abstract":[{"text":"The eigenvalue density of many large random matrices is well approximated by a deterministic measure, the self-consistent density of states. In the present work, we show this behaviour for several classes of random matrices. In fact, we establish that, in each of these classes, the self-consistent density of states approximates the eigenvalue density of the random matrix on all scales slightly above the typical eigenvalue spacing. For large classes of random matrices, the self-consistent density of states exhibits several universal features. We prove that, under suitable assumptions, random Gram matrices and Hermitian random matrices with decaying correlations have a 1/3-Hölder continuous self-consistent density of states ρ on R, which is analytic, where it is positive, and has either a square root edge or a cubic root cusp, where it vanishes. We, thus, extend the validity of the corresponding result for Wigner-type matrices from [4, 5, 7]. We show that ρ is determined as the inverse Stieltjes transform of the normalized trace of the unique solution m(z) to the Dyson equation −m(z) −1 = z − a + S[m(z)] on C N×N with the constraint Im m(z) ≥ 0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of C N×N and S is a positivity-preserving operator on C N×N encoding the first two moments of the random matrix. In order to analyze a possible limit of ρ for N → ∞ and address some applications in free probability theory, we also consider the Dyson equation on infinite dimensional von Neumann algebras. We present two applications to random matrices. We first establish that, under certain assumptions, large random matrices with independent entries have a rotationally symmetric self-consistent density of states which is supported on a centered disk in C. Moreover, it is infinitely often differentiable apart from a jump on the boundary of this disk. Second, we show edge universality at all regular (not necessarily extreme) spectral edges for Hermitian random matrices with decaying correlations.","lang":"eng"}],"ec_funded":1,"related_material":{"record":[{"relation":"part_of_dissertation","id":"1677","status":"public"},{"relation":"part_of_dissertation","id":"550","status":"public"},{"relation":"part_of_dissertation","status":"public","id":"6183"},{"relation":"part_of_dissertation","id":"566","status":"public"},{"id":"1010","status":"public","relation":"part_of_dissertation"},{"relation":"part_of_dissertation","status":"public","id":"6240"},{"id":"6184","status":"public","relation":"part_of_dissertation"}]},"language":[{"iso":"eng"}],"file":[{"creator":"dernst","file_size":5801709,"date_updated":"2020-07-14T12:44:57Z","file_name":"2018_thesis_Alt.pdf","date_created":"2019-04-08T13:55:20Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"6241","checksum":"d4dad55a7513f345706aaaba90cb1bb8"},{"file_id":"6242","checksum":"d73fcf46300dce74c403f2b491148ab4","access_level":"closed","relation":"source_file","content_type":"application/zip","date_created":"2019-04-08T13:55:20Z","file_name":"2018_thesis_Alt_source.zip","creator":"dernst","date_updated":"2020-07-14T12:44:57Z","file_size":3802059}],"degree_awarded":"PhD","publication_status":"published","publication_identifier":{"issn":["2663-337X"]},"project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"title":"Dyson equation and eigenvalue statistics of random matrices","article_processing_charge":"No","author":[{"last_name":"Alt","full_name":"Alt, Johannes","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"7772","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"short":"J. Alt, Dyson Equation and Eigenvalue Statistics of Random Matrices, Institute of Science and Technology Austria, 2018.","ieee":"J. Alt, “Dyson equation and eigenvalue statistics of random matrices,” Institute of Science and Technology Austria, 2018.","apa":"Alt, J. (2018). Dyson equation and eigenvalue statistics of random matrices. Institute of Science and Technology Austria. https://doi.org/10.15479/AT:ISTA:TH_1040","ama":"Alt J. Dyson equation and eigenvalue statistics of random matrices. 2018. doi:10.15479/AT:ISTA:TH_1040","mla":"Alt, Johannes. Dyson Equation and Eigenvalue Statistics of Random Matrices. Institute of Science and Technology Austria, 2018, doi:10.15479/AT:ISTA:TH_1040.","ista":"Alt J. 2018. Dyson equation and eigenvalue statistics of random matrices. Institute of Science and Technology Austria.","chicago":"Alt, Johannes. “Dyson Equation and Eigenvalue Statistics of Random Matrices.” Institute of Science and Technology Austria, 2018. https://doi.org/10.15479/AT:ISTA:TH_1040."},"oa":1,"publisher":"Institute of Science and Technology Austria","date_created":"2018-12-11T11:44:53Z","date_published":"2018-07-12T00:00:00Z","doi":"10.15479/AT:ISTA:TH_1040","page":"456","day":"12","year":"2018","has_accepted_license":"1"},{"_id":"483","type":"journal_article","status":"public","date_updated":"2021-01-12T08:00:57Z","department":[{"_id":"LaEr"}],"abstract":[{"text":"We prove the universality for the eigenvalue gap statistics in the bulk of the spectrum for band matrices, in the regime where the band width is comparable with the dimension of the matrix, W ~ N. All previous results concerning universality of non-Gaussian random matrices are for mean-field models. By relying on a new mean-field reduction technique, we deduce universality from quantum unique ergodicity for band matrices.","lang":"eng"}],"oa_version":"Submitted Version","main_file_link":[{"url":"https://arxiv.org/abs/1602.02312","open_access":"1"}],"scopus_import":1,"intvolume":" 21","month":"08","publication_status":"published","publication_identifier":{"issn":["10950761"]},"language":[{"iso":"eng"}],"ec_funded":1,"volume":21,"issue":"3","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"citation":{"short":"P. Bourgade, L. Erdös, H. Yau, J. Yin, Advances in Theoretical and Mathematical Physics 21 (2017) 739–800.","ieee":"P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Universality for a class of random band matrices,” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3. International Press, pp. 739–800, 2017.","ama":"Bourgade P, Erdös L, Yau H, Yin J. Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. 2017;21(3):739-800. doi:10.4310/ATMP.2017.v21.n3.a5","apa":"Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2017). Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. International Press. https://doi.org/10.4310/ATMP.2017.v21.n3.a5","mla":"Bourgade, Paul, et al. “Universality for a Class of Random Band Matrices.” Advances in Theoretical and Mathematical Physics, vol. 21, no. 3, International Press, 2017, pp. 739–800, doi:10.4310/ATMP.2017.v21.n3.a5.","ista":"Bourgade P, Erdös L, Yau H, Yin J. 2017. Universality for a class of random band matrices. Advances in Theoretical and Mathematical Physics. 21(3), 739–800.","chicago":"Bourgade, Paul, László Erdös, Horng Yau, and Jun Yin. “Universality for a Class of Random Band Matrices.” Advances in Theoretical and Mathematical Physics. International Press, 2017. https://doi.org/10.4310/ATMP.2017.v21.n3.a5."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"7337","author":[{"full_name":"Bourgade, Paul","last_name":"Bourgade","first_name":"Paul"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"first_name":"Horng","full_name":"Yau, Horng","last_name":"Yau"},{"last_name":"Yin","full_name":"Yin, Jun","first_name":"Jun"}],"title":"Universality for a class of random band matrices","oa":1,"quality_controlled":"1","publisher":"International Press","year":"2017","publication":"Advances in Theoretical and Mathematical Physics","day":"25","page":"739 - 800","date_created":"2018-12-11T11:46:43Z","doi":"10.4310/ATMP.2017.v21.n3.a5","date_published":"2017-08-25T00:00:00Z"},{"series_title":"Courant Lecture Notes","_id":"567","status":"public","type":"book","date_updated":"2022-05-24T06:57:28Z","department":[{"_id":"LaEr"}],"oa_version":"None","abstract":[{"text":"This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality.\r\n","lang":"eng"}],"month":"01","intvolume":" 28","alternative_title":["Courant Lecture Notes"],"language":[{"iso":"eng"}],"publication_identifier":{"isbn":["9-781-4704-3648-3"],"eisbn":["978-1-4704-4194-4"]},"publication_status":"published","volume":28,"ec_funded":1,"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Erdös L, Yau H. 2017. A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 226p.","chicago":"Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory. Vol. 28. Courant Lecture Notes. American Mathematical Society, 2017. https://doi.org/10.1090/cln/028.","ama":"Erdös L, Yau H. A Dynamical Approach to Random Matrix Theory. Vol 28. American Mathematical Society; 2017. doi:10.1090/cln/028","apa":"Erdös, L., & Yau, H. (2017). A Dynamical Approach to Random Matrix Theory (Vol. 28). American Mathematical Society. https://doi.org/10.1090/cln/028","ieee":"L. Erdös and H. Yau, A Dynamical Approach to Random Matrix Theory, vol. 28. American Mathematical Society, 2017.","short":"L. Erdös, H. Yau, A Dynamical Approach to Random Matrix Theory, American Mathematical Society, 2017.","mla":"Erdös, László, and Horng Yau. A Dynamical Approach to Random Matrix Theory. Vol. 28, American Mathematical Society, 2017, doi:10.1090/cln/028."},"title":"A Dynamical Approach to Random Matrix Theory","author":[{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Horng","last_name":"Yau","full_name":"Yau, Horng"}],"publist_id":"7247","article_processing_charge":"No","quality_controlled":"1","publisher":"American Mathematical Society","day":"01","year":"2017","date_published":"2017-01-01T00:00:00Z","doi":"10.1090/cln/028","date_created":"2018-12-11T11:47:13Z","page":"226"},{"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"doi":"10.1214/16-AIHP765","date_published":"2017-11-01T00:00:00Z","date_created":"2018-12-11T11:47:30Z","page":"1606 - 1656","day":"01","publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","year":"2017","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"title":"Universality for random matrix flows with time dependent density","publist_id":"7189","author":[{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","last_name":"Schnelli","first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Erdös L, Schnelli K. 2017. Universality for random matrix flows with time dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics. 53(4), 1606–1656.","chicago":"Erdös, László, and Kevin Schnelli. “Universality for Random Matrix Flows with Time Dependent Density.” Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-AIHP765.","ama":"Erdös L, Schnelli K. Universality for random matrix flows with time dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics. 2017;53(4):1606-1656. doi:10.1214/16-AIHP765","apa":"Erdös, L., & Schnelli, K. (2017). Universality for random matrix flows with time dependent density. Annales de l’institut Henri Poincare (B) Probability and Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/16-AIHP765","ieee":"L. Erdös and K. Schnelli, “Universality for random matrix flows with time dependent density,” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 53, no. 4. Institute of Mathematical Statistics, pp. 1606–1656, 2017.","short":"L. Erdös, K. Schnelli, Annales de l’institut Henri Poincare (B) Probability and Statistics 53 (2017) 1606–1656.","mla":"Erdös, László, and Kevin Schnelli. “Universality for Random Matrix Flows with Time Dependent Density.” Annales de l’institut Henri Poincare (B) Probability and Statistics, vol. 53, no. 4, Institute of Mathematical Statistics, 2017, pp. 1606–56, doi:10.1214/16-AIHP765."},"month":"11","intvolume":" 53","scopus_import":1,"main_file_link":[{"url":"https://arxiv.org/abs/1504.00650","open_access":"1"}],"oa_version":"Submitted Version","abstract":[{"text":"We show that the Dyson Brownian Motion exhibits local universality after a very short time assuming that local rigidity and level repulsion of the eigenvalues hold. These conditions are verified, hence bulk spectral universality is proven, for a large class of Wigner-like matrices, including deformed Wigner ensembles and ensembles with non-stochastic variance matrices whose limiting densities differ from Wigner's semicircle law.","lang":"eng"}],"volume":53,"issue":"4","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["02460203"]},"publication_status":"published","status":"public","type":"journal_article","_id":"615","department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T08:06:22Z"},{"oa":1,"quality_controlled":"1","publisher":"Wiley-Blackwell","date_created":"2018-12-11T11:48:08Z","doi":"10.1002/cpa.21639","date_published":"2017-09-01T00:00:00Z","page":"1672 - 1705","publication":"Communications on Pure and Applied Mathematics","day":"01","year":"2017","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"title":"Singularities of solutions to quadratic vector equations on the complex upper half plane","author":[{"full_name":"Ajanki, Oskari H","last_name":"Ajanki","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","first_name":"Oskari H"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"6959","user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"mla":"Ajanki, Oskari H., et al. “Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half Plane.” Communications on Pure and Applied Mathematics, vol. 70, no. 9, Wiley-Blackwell, 2017, pp. 1672–705, doi:10.1002/cpa.21639.","apa":"Ajanki, O. H., Krüger, T. H., & Erdös, L. (2017). Singularities of solutions to quadratic vector equations on the complex upper half plane. Communications on Pure and Applied Mathematics. Wiley-Blackwell. https://doi.org/10.1002/cpa.21639","ama":"Ajanki OH, Krüger TH, Erdös L. Singularities of solutions to quadratic vector equations on the complex upper half plane. Communications on Pure and Applied Mathematics. 2017;70(9):1672-1705. doi:10.1002/cpa.21639","short":"O.H. Ajanki, T.H. Krüger, L. Erdös, Communications on Pure and Applied Mathematics 70 (2017) 1672–1705.","ieee":"O. H. Ajanki, T. H. Krüger, and L. Erdös, “Singularities of solutions to quadratic vector equations on the complex upper half plane,” Communications on Pure and Applied Mathematics, vol. 70, no. 9. Wiley-Blackwell, pp. 1672–1705, 2017.","chicago":"Ajanki, Oskari H, Torben H Krüger, and László Erdös. “Singularities of Solutions to Quadratic Vector Equations on the Complex Upper Half Plane.” Communications on Pure and Applied Mathematics. Wiley-Blackwell, 2017. https://doi.org/10.1002/cpa.21639.","ista":"Ajanki OH, Krüger TH, Erdös L. 2017. Singularities of solutions to quadratic vector equations on the complex upper half plane. Communications on Pure and Applied Mathematics. 70(9), 1672–1705."},"intvolume":" 70","month":"09","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1512.03703"}],"scopus_import":1,"oa_version":"Submitted Version","abstract":[{"text":"Let S be a positivity-preserving symmetric linear operator acting on bounded functions. The nonlinear equation -1/m=z+Sm with a parameter z in the complex upper half-plane ℍ has a unique solution m with values in ℍ. We show that the z-dependence of this solution can be represented as the Stieltjes transforms of a family of probability measures v on ℝ. Under suitable conditions on S, we show that v has a real analytic density apart from finitely many algebraic singularities of degree at most 3. Our motivation comes from large random matrices. The solution m determines the density of eigenvalues of two prominent matrix ensembles: (i) matrices with centered independent entries whose variances are given by S and (ii) matrices with correlated entries with a translation-invariant correlation structure. Our analysis shows that the limiting eigenvalue density has only square root singularities or cubic root cusps; no other singularities occur.","lang":"eng"}],"ec_funded":1,"volume":70,"issue":"9","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["00103640"]},"status":"public","type":"journal_article","_id":"721","department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T08:12:24Z"},{"oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","year":"2017","has_accepted_license":"1","publication":"Electronic Communications in Probability","day":"21","date_created":"2018-12-11T11:47:07Z","doi":"10.1214/17-ECP97","date_published":"2017-11-21T00:00:00Z","article_number":"63","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"citation":{"ieee":"J. Alt, “Singularities of the density of states of random Gram matrices,” Electronic Communications in Probability, vol. 22. Institute of Mathematical Statistics, 2017.","short":"J. Alt, Electronic Communications in Probability 22 (2017).","ama":"Alt J. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 2017;22. doi:10.1214/17-ECP97","apa":"Alt, J. (2017). Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/17-ECP97","mla":"Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.” Electronic Communications in Probability, vol. 22, 63, Institute of Mathematical Statistics, 2017, doi:10.1214/17-ECP97.","ista":"Alt J. 2017. Singularities of the density of states of random Gram matrices. Electronic Communications in Probability. 22, 63.","chicago":"Alt, Johannes. “Singularities of the Density of States of Random Gram Matrices.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-ECP97."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes","full_name":"Alt, Johannes","last_name":"Alt"}],"publist_id":"7265","title":"Singularities of the density of states of random Gram matrices","abstract":[{"text":"For large random matrices X with independent, centered entries but not necessarily identical variances, the eigenvalue density of XX* is well-approximated by a deterministic measure on ℝ. We show that the density of this measure has only square and cubic-root singularities away from zero. We also extend the bulk local law in [5] to the vicinity of these singularities.","lang":"eng"}],"oa_version":"Published Version","scopus_import":1,"intvolume":" 22","month":"11","publication_status":"published","publication_identifier":{"issn":["1083589X"]},"language":[{"iso":"eng"}],"file":[{"creator":"system","file_size":470876,"date_updated":"2020-07-14T12:47:00Z","file_name":"IST-2018-926-v1+1_euclid.ecp.1511233247.pdf","date_created":"2018-12-12T10:08:04Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_id":"4663","checksum":"0ec05303a0de190de145654237984c79"}],"ec_funded":1,"volume":22,"related_material":{"record":[{"status":"public","id":"149","relation":"dissertation_contains"}]},"_id":"550","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","pubrep_id":"926","status":"public","date_updated":"2023-09-07T12:38:08Z","ddc":["539"],"department":[{"_id":"LaEr"}],"file_date_updated":"2020-07-14T12:47:00Z"},{"project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_number":"86","author":[{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"publist_id":"6214","title":"Fluctuations of functions of Wigner matrices","citation":{"mla":"Erdös, László, and Dominik J. Schröder. “Fluctuations of Functions of Wigner Matrices.” Electronic Communications in Probability, vol. 21, 86, Institute of Mathematical Statistics, 2017, doi:10.1214/16-ECP38.","short":"L. Erdös, D.J. Schröder, Electronic Communications in Probability 21 (2017).","ieee":"L. Erdös and D. J. Schröder, “Fluctuations of functions of Wigner matrices,” Electronic Communications in Probability, vol. 21. Institute of Mathematical Statistics, 2017.","ama":"Erdös L, Schröder DJ. Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. 2017;21. doi:10.1214/16-ECP38","apa":"Erdös, L., & Schröder, D. J. (2017). Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/16-ECP38","chicago":"Erdös, László, and Dominik J Schröder. “Fluctuations of Functions of Wigner Matrices.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/16-ECP38.","ista":"Erdös L, Schröder DJ. 2017. Fluctuations of functions of Wigner matrices. Electronic Communications in Probability. 21, 86."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"acknowledgement":"Partially supported by the IST Austria Excellence Scholarship.","date_published":"2017-01-02T00:00:00Z","doi":"10.1214/16-ECP38","date_created":"2018-12-11T11:50:23Z","has_accepted_license":"1","year":"2017","day":"02","publication":"Electronic Communications in Probability","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","pubrep_id":"747","_id":"1144","department":[{"_id":"LaEr"}],"file_date_updated":"2018-12-12T10:18:10Z","date_updated":"2023-09-07T12:54:12Z","ddc":["510"],"scopus_import":1,"month":"01","intvolume":" 21","abstract":[{"text":"We show that matrix elements of functions of N × N Wigner matrices fluctuate on a scale of order N−1/2 and we identify the limiting fluctuation. Our result holds for any function f of the matrix that has bounded variation thus considerably relaxing the regularity requirement imposed in [7, 11].","lang":"eng"}],"oa_version":"Published Version","volume":21,"related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"}]},"ec_funded":1,"publication_status":"published","file":[{"date_created":"2018-12-12T10:18:10Z","file_name":"IST-2017-747-v1+1_euclid.ecp.1483347665.pdf","date_updated":"2018-12-12T10:18:10Z","file_size":440770,"creator":"system","file_id":"5329","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}]},{"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block Band Matrices.” Probability Theory and Related Fields, vol. 167, no. 3–4, Springer, 2017, pp. 673–776, doi:10.1007/s00440-015-0692-y.","apa":"Bao, Z., & Erdös, L. (2017). Delocalization for a class of random block band matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-015-0692-y","ama":"Bao Z, Erdös L. Delocalization for a class of random block band matrices. Probability Theory and Related Fields. 2017;167(3-4):673-776. doi:10.1007/s00440-015-0692-y","short":"Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 673–776.","ieee":"Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,” Probability Theory and Related Fields, vol. 167, no. 3–4. Springer, pp. 673–776, 2017.","chicago":"Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block Band Matrices.” Probability Theory and Related Fields. Springer, 2017. https://doi.org/10.1007/s00440-015-0692-y.","ista":"Bao Z, Erdös L. 2017. Delocalization for a class of random block band matrices. Probability Theory and Related Fields. 167(3–4), 673–776."},"title":"Delocalization for a class of random block band matrices","external_id":{"isi":["000398842700004"]},"article_processing_charge":"Yes (via OA deal)","publist_id":"5644","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang","last_name":"Bao","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"}],"acknowledgement":"Z. Bao was supported by ERC Advanced Grant RANMAT No. 338804; L. Erdős was partially supported by ERC Advanced Grant RANMAT No. 338804.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to the anonymous referees for careful reading and valuable comments, which helped to improve the organization.","oa":1,"quality_controlled":"1","publisher":"Springer","publication":"Probability Theory and Related Fields","day":"01","year":"2017","has_accepted_license":"1","isi":1,"date_created":"2018-12-11T11:52:32Z","doi":"10.1007/s00440-015-0692-y","date_published":"2017-04-01T00:00:00Z","page":"673 - 776","_id":"1528","pubrep_id":"489","status":"public","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","type":"journal_article","ddc":["530"],"date_updated":"2023-09-20T09:42:12Z","department":[{"_id":"LaEr"}],"file_date_updated":"2020-07-14T12:45:00Z","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We consider N×N Hermitian random matrices H consisting of blocks of size M≥N6/7. The matrix elements are i.i.d. within the blocks, close to a Gaussian in the four moment matching sense, but their distribution varies from block to block to form a block-band structure, with an essential band width M. We show that the entries of the Green’s function G(z)=(H−z)−1 satisfy the local semicircle law with spectral parameter z=E+iη down to the real axis for any η≫N−1, using a combination of the supersymmetry method inspired by Shcherbina (J Stat Phys 155(3): 466–499, 2014) and the Green’s function comparison strategy. Previous estimates were valid only for η≫M−1. The new estimate also implies that the eigenvectors in the middle of the spectrum are fully delocalized."}],"intvolume":" 167","month":"04","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"file_name":"IST-2016-489-v1+1_s00440-015-0692-y.pdf","date_created":"2018-12-12T10:08:05Z","creator":"system","file_size":1615755,"date_updated":"2020-07-14T12:45:00Z","checksum":"67afa85ff1e220cbc1f9f477a828513c","file_id":"4665","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"issn":["01788051"]},"ec_funded":1,"issue":"3-4","volume":167},{"department":[{"_id":"LaEr"}],"file_date_updated":"2020-07-14T12:44:44Z","date_updated":"2023-09-20T11:14:17Z","ddc":["510","530"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","pubrep_id":"657","status":"public","_id":"1337","ec_funded":1,"issue":"3-4","volume":169,"publication_status":"published","publication_identifier":{"issn":["01788051"]},"language":[{"iso":"eng"}],"file":[{"file_name":"IST-2017-657-v1+2_s00440-016-0740-2.pdf","date_created":"2018-12-12T10:08:25Z","file_size":988843,"date_updated":"2020-07-14T12:44:44Z","creator":"system","file_id":"4686","checksum":"29f5a72c3f91e408aeb9e78344973803","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"scopus_import":"1","intvolume":" 169","month":"12","abstract":[{"text":"We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with centered independent entries. In contrast to previous works the matrix of variances sij=\\mathbbmE|hij|2 is not assumed to be stochastic. Hence the density of states is not the Wigner semicircle law. Its possible shapes are described in the companion paper (Ajanki et al. in Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the resolvent, G(z)=(H−z)−1, converges to a diagonal matrix, diag(m(z)), where m(z)=(m1(z),…,mN(z)) solves the vector equation −1/mi(z)=z+∑jsijmj(z) that has been analyzed in Ajanki et al. (Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We prove a local law down to the smallest spectral resolution scale, and bulk universality for both real symmetric and complex hermitian symmetry classes.","lang":"eng"}],"oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000414358400002"]},"author":[{"full_name":"Ajanki, Oskari H","last_name":"Ajanki","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","first_name":"Oskari H"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger"}],"publist_id":"5930","title":"Universality for general Wigner-type matrices","citation":{"apa":"Ajanki, O. H., Erdös, L., & Krüger, T. H. (2017). Universality for general Wigner-type matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-016-0740-2","ama":"Ajanki OH, Erdös L, Krüger TH. Universality for general Wigner-type matrices. Probability Theory and Related Fields. 2017;169(3-4):667-727. doi:10.1007/s00440-016-0740-2","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 169 (2017) 667–727.","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Universality for general Wigner-type matrices,” Probability Theory and Related Fields, vol. 169, no. 3–4. Springer, pp. 667–727, 2017.","mla":"Ajanki, Oskari H., et al. “Universality for General Wigner-Type Matrices.” Probability Theory and Related Fields, vol. 169, no. 3–4, Springer, 2017, pp. 667–727, doi:10.1007/s00440-016-0740-2.","ista":"Ajanki OH, Erdös L, Krüger TH. 2017. Universality for general Wigner-type matrices. Probability Theory and Related Fields. 169(3–4), 667–727.","chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Universality for General Wigner-Type Matrices.” Probability Theory and Related Fields. Springer, 2017. https://doi.org/10.1007/s00440-016-0740-2."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"page":"667 - 727","date_created":"2018-12-11T11:51:27Z","date_published":"2017-12-01T00:00:00Z","doi":"10.1007/s00440-016-0740-2","year":"2017","isi":1,"has_accepted_license":"1","publication":"Probability Theory and Related Fields","day":"01","oa":1,"publisher":"Springer","quality_controlled":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). "},{"doi":"10.1007/s00220-016-2805-6","date_published":"2017-02-01T00:00:00Z","date_created":"2018-12-11T11:50:43Z","page":"947 - 990","day":"01","publication":"Communications in Mathematical Physics","has_accepted_license":"1","isi":1,"year":"2017","quality_controlled":"1","publisher":"Springer","oa":1,"title":"Local law of addition of random matrices on optimal scale","publist_id":"6141","author":[{"full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin"}],"external_id":{"isi":["000393696700005"]},"article_processing_charge":"Yes (via OA deal)","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Bao, Zhigang, et al. “Local Law of Addition of Random Matrices on Optimal Scale.” Communications in Mathematical Physics, vol. 349, no. 3, Springer, 2017, pp. 947–90, doi:10.1007/s00220-016-2805-6.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2017). Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-016-2805-6","ama":"Bao Z, Erdös L, Schnelli K. Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. 2017;349(3):947-990. doi:10.1007/s00220-016-2805-6","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local law of addition of random matrices on optimal scale,” Communications in Mathematical Physics, vol. 349, no. 3. Springer, pp. 947–990, 2017.","short":"Z. Bao, L. Erdös, K. Schnelli, Communications in Mathematical Physics 349 (2017) 947–990.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Law of Addition of Random Matrices on Optimal Scale.” Communications in Mathematical Physics. Springer, 2017. https://doi.org/10.1007/s00220-016-2805-6.","ista":"Bao Z, Erdös L, Schnelli K. 2017. Local law of addition of random matrices on optimal scale. Communications in Mathematical Physics. 349(3), 947–990."},"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"issue":"3","volume":349,"ec_funded":1,"file":[{"checksum":"ddff79154c3daf27237de5383b1264a9","file_id":"5102","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2018-12-12T10:14:47Z","file_name":"IST-2016-722-v1+1_s00220-016-2805-6.pdf","date_updated":"2020-07-14T12:44:39Z","file_size":1033743,"creator":"system"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["00103616"]},"publication_status":"published","month":"02","intvolume":" 349","scopus_import":"1","oa_version":"Published Version","abstract":[{"text":"The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free convolution of their spectral distributions. We prove that this convergence also holds locally in the bulk of the spectrum, down to the optimal scales larger than the eigenvalue spacing. The corresponding eigenvectors are fully delocalized. Similar results hold for the sum of two real symmetric matrices, when one is conjugated by Haar orthogonal matrix.","lang":"eng"}],"department":[{"_id":"LaEr"}],"file_date_updated":"2020-07-14T12:44:39Z","ddc":["530"],"date_updated":"2023-09-20T11:16:57Z","status":"public","pubrep_id":"722","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"1207"},{"_id":"1023","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","pubrep_id":"802","status":"public","date_updated":"2023-09-22T09:27:51Z","ddc":["510"],"file_date_updated":"2018-12-12T10:15:29Z","department":[{"_id":"LaEr"}],"abstract":[{"text":"We consider products of independent square non-Hermitian random matrices. More precisely, let X1,…, Xn be independent N × N random matrices with independent entries (real or complex with independent real and imaginary parts) with zero mean and variance 1/N. Soshnikov-O’Rourke [19] and Götze-Tikhomirov [15] showed that the empirical spectral distribution of the product of n random matrices with iid entries converges to (equation found). We prove that if the entries of the matrices X1,…, Xn are independent (but not necessarily identically distributed) and satisfy uniform subexponential decay condition, then in the bulk the convergence of the ESD of X1,…, Xn to (0.1) holds up to the scale N–1/2+ε.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 22","month":"02","publication_status":"published","publication_identifier":{"issn":["10836489"]},"language":[{"iso":"eng"}],"file":[{"file_id":"5149","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"IST-2017-802-v1+1_euclid.ejp.1487991681.pdf","date_created":"2018-12-12T10:15:29Z","file_size":742275,"date_updated":"2018-12-12T10:15:29Z","creator":"system"}],"volume":22,"article_number":"22","citation":{"mla":"Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian Random Matrices with Independent Entries.” Electronic Journal of Probability, vol. 22, 22, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP38.","ieee":"Y. Nemish, “Local law for the product of independent non-Hermitian random matrices with independent entries,” Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics, 2017.","short":"Y. Nemish, Electronic Journal of Probability 22 (2017).","apa":"Nemish, Y. (2017). Local law for the product of independent non-Hermitian random matrices with independent entries. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/17-EJP38","ama":"Nemish Y. Local law for the product of independent non-Hermitian random matrices with independent entries. Electronic Journal of Probability. 2017;22. doi:10.1214/17-EJP38","chicago":"Nemish, Yuriy. “Local Law for the Product of Independent Non-Hermitian Random Matrices with Independent Entries.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-EJP38.","ista":"Nemish Y. 2017. Local law for the product of independent non-Hermitian random matrices with independent entries. Electronic Journal of Probability. 22, 22."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","external_id":{"isi":["000396611900022"]},"article_processing_charge":"No","publist_id":"6370","author":[{"first_name":"Yuriy","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","last_name":"Nemish","orcid":"0000-0002-7327-856X","full_name":"Nemish, Yuriy"}],"title":"Local law for the product of independent non-Hermitian random matrices with independent entries","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","year":"2017","isi":1,"has_accepted_license":"1","publication":"Electronic Journal of Probability","day":"06","date_created":"2018-12-11T11:49:44Z","date_published":"2017-02-06T00:00:00Z","doi":"10.1214/17-EJP38"},{"status":"public","pubrep_id":"807","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"1010","department":[{"_id":"LaEr"}],"file_date_updated":"2018-12-12T10:13:39Z","ddc":["510","539"],"date_updated":"2023-09-22T09:45:23Z","month":"03","intvolume":" 22","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","text":"We prove a local law in the bulk of the spectrum for random Gram matrices XX∗, a generalization of sample covariance matrices, where X is a large matrix with independent, centered entries with arbitrary variances. The limiting eigenvalue density that generalizes the Marchenko-Pastur law is determined by solving a system of nonlinear equations. Our entrywise and averaged local laws are on the optimal scale with the optimal error bounds. They hold both in the square case (hard edge) and in the properly rectangular case (soft edge). In the latter case we also establish a macroscopic gap away from zero in the spectrum of XX∗. "}],"volume":22,"related_material":{"record":[{"id":"149","status":"public","relation":"dissertation_contains"}]},"ec_funded":1,"file":[{"file_size":639384,"date_updated":"2018-12-12T10:13:39Z","creator":"system","file_name":"IST-2017-807-v1+1_euclid.ejp.1488942016.pdf","date_created":"2018-12-12T10:13:39Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"5024"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["10836489"]},"publication_status":"published","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_number":"25","title":"Local law for random Gram matrices","author":[{"last_name":"Alt","full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"6386","external_id":{"isi":["000396611900025"],"arxiv":["1606.07353"]},"article_processing_charge":"No","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"apa":"Alt, J., Erdös, L., & Krüger, T. H. (2017). Local law for random Gram matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/17-EJP42","ama":"Alt J, Erdös L, Krüger TH. Local law for random Gram matrices. Electronic Journal of Probability. 2017;22. doi:10.1214/17-EJP42","short":"J. Alt, L. Erdös, T.H. Krüger, Electronic Journal of Probability 22 (2017).","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Local law for random Gram matrices,” Electronic Journal of Probability, vol. 22. Institute of Mathematical Statistics, 2017.","mla":"Alt, Johannes, et al. “Local Law for Random Gram Matrices.” Electronic Journal of Probability, vol. 22, 25, Institute of Mathematical Statistics, 2017, doi:10.1214/17-EJP42.","ista":"Alt J, Erdös L, Krüger TH. 2017. Local law for random Gram matrices. Electronic Journal of Probability. 22, 25.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Local Law for Random Gram Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2017. https://doi.org/10.1214/17-EJP42."},"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"date_published":"2017-03-08T00:00:00Z","doi":"10.1214/17-EJP42","date_created":"2018-12-11T11:49:40Z","day":"08","publication":"Electronic Journal of Probability","has_accepted_license":"1","isi":1,"year":"2017"},{"project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"publist_id":"6935","author":[{"last_name":"Bao","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231"}],"article_processing_charge":"No","external_id":{"isi":["000412150400010"]},"title":"Convergence rate for spectral distribution of addition of random matrices","citation":{"chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” Advances in Mathematics. Academic Press, 2017. https://doi.org/10.1016/j.aim.2017.08.028.","ista":"Bao Z, Erdös L, Schnelli K. 2017. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 319, 251–291.","mla":"Bao, Zhigang, et al. “Convergence Rate for Spectral Distribution of Addition of Random Matrices.” Advances in Mathematics, vol. 319, Academic Press, 2017, pp. 251–91, doi:10.1016/j.aim.2017.08.028.","ama":"Bao Z, Erdös L, Schnelli K. Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. 2017;319:251-291. doi:10.1016/j.aim.2017.08.028","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2017). Convergence rate for spectral distribution of addition of random matrices. Advances in Mathematics. Academic Press. https://doi.org/10.1016/j.aim.2017.08.028","short":"Z. Bao, L. Erdös, K. Schnelli, Advances in Mathematics 319 (2017) 251–291.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Convergence rate for spectral distribution of addition of random matrices,” Advances in Mathematics, vol. 319. Academic Press, pp. 251–291, 2017."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","publisher":"Academic Press","quality_controlled":"1","oa":1,"acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804, Hong Kong RGC grant ECS 26301517, and the Göran Gustafsson Foundation","page":"251 - 291","date_published":"2017-10-15T00:00:00Z","doi":"10.1016/j.aim.2017.08.028","date_created":"2018-12-11T11:48:13Z","isi":1,"year":"2017","day":"15","publication":"Advances in Mathematics","type":"journal_article","status":"public","_id":"733","department":[{"_id":"LaEr"}],"date_updated":"2023-09-28T11:30:42Z","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1606.03076","open_access":"1"}],"month":"10","intvolume":" 319","abstract":[{"text":"Let A and B be two N by N deterministic Hermitian matrices and let U be an N by N Haar distributed unitary matrix. It is well known that the spectral distribution of the sum H = A + UBU∗ converges weakly to the free additive convolution of the spectral distributions of A and B, as N tends to infinity. We establish the optimal convergence rate in the bulk of the spectrum.","lang":"eng"}],"oa_version":"Submitted Version","volume":319,"ec_funded":1,"publication_status":"published","language":[{"iso":"eng"}]},{"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"title":"Fluctuations of the competition interface in presence of shocks","author":[{"first_name":"Patrik","full_name":"Ferrari, Patrik","last_name":"Ferrari"},{"id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","first_name":"Peter","full_name":"Nejjar, Peter","last_name":"Nejjar"}],"publist_id":"7376","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"P. Ferrari, P. Nejjar, Revista Latino-Americana de Probabilidade e Estatística 9 (2017) 299–325.","ieee":"P. Ferrari and P. Nejjar, “Fluctuations of the competition interface in presence of shocks,” Revista Latino-Americana de Probabilidade e Estatística, vol. 9. Instituto Nacional de Matematica Pura e Aplicada, pp. 299–325, 2017.","apa":"Ferrari, P., & Nejjar, P. (2017). Fluctuations of the competition interface in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística. Instituto Nacional de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.v14-17","ama":"Ferrari P, Nejjar P. Fluctuations of the competition interface in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística. 2017;9:299-325. doi:10.30757/ALEA.v14-17","mla":"Ferrari, Patrik, and Peter Nejjar. “Fluctuations of the Competition Interface in Presence of Shocks.” Revista Latino-Americana de Probabilidade e Estatística, vol. 9, Instituto Nacional de Matematica Pura e Aplicada, 2017, pp. 299–325, doi:10.30757/ALEA.v14-17.","ista":"Ferrari P, Nejjar P. 2017. Fluctuations of the competition interface in presence of shocks. Revista Latino-Americana de Probabilidade e Estatística. 9, 299–325.","chicago":"Ferrari, Patrik, and Peter Nejjar. “Fluctuations of the Competition Interface in Presence of Shocks.” Revista Latino-Americana de Probabilidade e Estatística. Instituto Nacional de Matematica Pura e Aplicada, 2017. https://doi.org/10.30757/ALEA.v14-17."},"quality_controlled":"1","publisher":"Instituto Nacional de Matematica Pura e Aplicada","oa":1,"date_published":"2017-03-23T00:00:00Z","doi":"10.30757/ALEA.v14-17","date_created":"2018-12-11T11:46:31Z","page":"299 - 325","day":"23","publication":"Revista Latino-Americana de Probabilidade e Estatística","year":"2017","status":"public","article_type":"original","type":"journal_article","_id":"447","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"date_updated":"2023-10-10T13:10:32Z","month":"03","intvolume":" 9","scopus_import":"1","main_file_link":[{"url":"http://alea.impa.br/articles/v14/14-17.pdf","open_access":"1"}],"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"We consider last passage percolation (LPP) models with exponentially distributed random variables, which are linked to the totally asymmetric simple exclusion process (TASEP). The competition interface for LPP was introduced and studied in Ferrari and Pimentel (2005a) for cases where the corresponding exclusion process had a rarefaction fan. Here we consider situations with a shock and determine the law of the fluctuations of the competition interface around its deter- ministic law of large number position. We also study the multipoint distribution of the LPP around the shock, extending our one-point result of Ferrari and Nejjar (2015)."}],"volume":9,"ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published"},{"acknowledgement":"We thank Horng-Tzer Yau for numerous discussions and remarks. We are grateful to Ben Adlam, Jinho Baik, Zhigang Bao, Paul Bourgade, László Erd ̋os, Iain Johnstone and Antti Knowles for comments. We are also grate-\r\nful to the anonymous referee for carefully reading our manuscript and suggesting several improvements.","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","publication":"Annals of Applied Probability","day":"15","year":"2016","date_created":"2018-12-11T11:50:27Z","doi":"10.1214/16-AAP1193","date_published":"2016-12-15T00:00:00Z","page":"3786 - 3839","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Lee J, Schnelli K. 2016. Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population. Annals of Applied Probability. 26(6), 3786–3839.","chicago":"Lee, Ji, and Kevin Schnelli. “Tracy-Widom Distribution for the Largest Eigenvalue of Real Sample Covariance Matrices with General Population.” Annals of Applied Probability. Institute of Mathematical Statistics, 2016. https://doi.org/10.1214/16-AAP1193.","ieee":"J. Lee and K. Schnelli, “Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population,” Annals of Applied Probability, vol. 26, no. 6. Institute of Mathematical Statistics, pp. 3786–3839, 2016.","short":"J. Lee, K. Schnelli, Annals of Applied Probability 26 (2016) 3786–3839.","apa":"Lee, J., & Schnelli, K. (2016). Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population. Annals of Applied Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/16-AAP1193","ama":"Lee J, Schnelli K. Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population. Annals of Applied Probability. 2016;26(6):3786-3839. doi:10.1214/16-AAP1193","mla":"Lee, Ji, and Kevin Schnelli. “Tracy-Widom Distribution for the Largest Eigenvalue of Real Sample Covariance Matrices with General Population.” Annals of Applied Probability, vol. 26, no. 6, Institute of Mathematical Statistics, 2016, pp. 3786–839, doi:10.1214/16-AAP1193."},"title":"Tracy-widom distribution for the largest eigenvalue of real sample covariance matrices with general population","author":[{"last_name":"Lee","full_name":"Lee, Ji","first_name":"Ji"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin"}],"publist_id":"6201","oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider sample covariance matrices of the form Q = ( σ1/2X)(σ1/2X)∗, where the sample X is an M ×N random matrix whose entries are real independent random variables with variance 1/N and whereσ is an M × M positive-definite deterministic matrix. We analyze the asymptotic fluctuations of the largest rescaled eigenvalue of Q when both M and N tend to infinity with N/M →d ϵ (0,∞). For a large class of populations σ in the sub-critical regime, we show that the distribution of the largest rescaled eigenvalue of Q is given by the type-1 Tracy-Widom distribution under the additional assumptions that (1) either the entries of X are i.i.d. Gaussians or (2) that σ is diagonal and that the entries of X have a sub-exponential decay."}],"intvolume":" 26","month":"12","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1409.4979"}],"scopus_import":1,"language":[{"iso":"eng"}],"publication_status":"published","ec_funded":1,"volume":26,"issue":"6","_id":"1157","status":"public","type":"journal_article","date_updated":"2021-01-12T06:48:43Z","department":[{"_id":"LaEr"}]},{"abstract":[{"lang":"eng","text":"We consider N×N random matrices of the form H = W + V where W is a real symmetric or complex Hermitian Wigner matrix and V is a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W, and we choose V so that the eigenvalues ofW and V are typically of the same order. For a large class of diagonal matrices V , we show that the local statistics in the bulk of the spectrum are universal in the limit of large N."}],"oa_version":"Preprint","scopus_import":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1405.6634"}],"month":"01","intvolume":" 44","publication_status":"published","language":[{"iso":"eng"}],"issue":"3","volume":44,"ec_funded":1,"_id":"1219","type":"journal_article","status":"public","date_updated":"2021-01-12T06:49:10Z","department":[{"_id":"LaEr"}],"acknowledgement":"J.C. was supported in part by National Research Foundation of Korea Grant 2011-0013474 and TJ Park Junior Faculty Fellowship.\r\nK.S. was supported by ERC Advanced Grant RANMAT, No. 338804, and the \"Fund for Math.\"\r\nB.S. was supported by NSF GRFP Fellowship DGE-1144152.\r\nH.Y. was supported in part by NSF Grant DMS-13-07444 and Simons investigator fellowship. We thank Paul Bourgade, László Erd ̋os and Antti Knowles for helpful comments. We are grateful to the Taida Institute for Mathematical\r\nSciences and National Taiwan Universality for their hospitality during part of this\r\nresearch. We thank Thomas Spencer and the Institute for Advanced Study for their\r\nhospitality during the academic year 2013–2014. ","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"year":"2016","day":"01","publication":"Annals of Probability","page":"2349 - 2425","date_published":"2016-01-01T00:00:00Z","doi":"10.1214/15-AOP1023","date_created":"2018-12-11T11:50:47Z","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"citation":{"ista":"Lee J, Schnelli K, Stetler B, Yau H. 2016. Bulk universality for deformed wigner matrices. Annals of Probability. 44(3), 2349–2425.","chicago":"Lee, Jioon, Kevin Schnelli, Ben Stetler, and Horngtzer Yau. “Bulk Universality for Deformed Wigner Matrices.” Annals of Probability. Institute of Mathematical Statistics, 2016. https://doi.org/10.1214/15-AOP1023.","short":"J. Lee, K. Schnelli, B. Stetler, H. Yau, Annals of Probability 44 (2016) 2349–2425.","ieee":"J. Lee, K. Schnelli, B. Stetler, and H. Yau, “Bulk universality for deformed wigner matrices,” Annals of Probability, vol. 44, no. 3. Institute of Mathematical Statistics, pp. 2349–2425, 2016.","apa":"Lee, J., Schnelli, K., Stetler, B., & Yau, H. (2016). Bulk universality for deformed wigner matrices. Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/15-AOP1023","ama":"Lee J, Schnelli K, Stetler B, Yau H. Bulk universality for deformed wigner matrices. Annals of Probability. 2016;44(3):2349-2425. doi:10.1214/15-AOP1023","mla":"Lee, Jioon, et al. “Bulk Universality for Deformed Wigner Matrices.” Annals of Probability, vol. 44, no. 3, Institute of Mathematical Statistics, 2016, pp. 2349–425, doi:10.1214/15-AOP1023."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publist_id":"6115","author":[{"last_name":"Lee","full_name":"Lee, Jioon","first_name":"Jioon"},{"first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231","last_name":"Schnelli"},{"full_name":"Stetler, Ben","last_name":"Stetler","first_name":"Ben"},{"last_name":"Yau","full_name":"Yau, Horngtzer","first_name":"Horngtzer"}],"title":"Bulk universality for deformed wigner matrices"},{"status":"public","type":"journal_article","_id":"1223","department":[{"_id":"LaEr"}],"title":"Localization for transversally periodic random potentials on binary trees","author":[{"last_name":"Froese","full_name":"Froese, Richard","first_name":"Richard"},{"first_name":"Darrick","last_name":"Lee","full_name":"Lee, Darrick"},{"last_name":"Sadel","full_name":"Sadel, Christian","orcid":"0000-0001-8255-3968","first_name":"Christian","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Spitzer","full_name":"Spitzer, Wolfgang","first_name":"Wolfgang"},{"first_name":"Günter","full_name":"Stolz, Günter","last_name":"Stolz"}],"publist_id":"6112","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:49:12Z","citation":{"apa":"Froese, R., Lee, D., Sadel, C., Spitzer, W., & Stolz, G. (2016). Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. European Mathematical Society. https://doi.org/10.4171/JST/132","ama":"Froese R, Lee D, Sadel C, Spitzer W, Stolz G. Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. 2016;6(3):557-600. doi:10.4171/JST/132","ieee":"R. Froese, D. Lee, C. Sadel, W. Spitzer, and G. Stolz, “Localization for transversally periodic random potentials on binary trees,” Journal of Spectral Theory, vol. 6, no. 3. European Mathematical Society, pp. 557–600, 2016.","short":"R. Froese, D. Lee, C. Sadel, W. Spitzer, G. Stolz, Journal of Spectral Theory 6 (2016) 557–600.","mla":"Froese, Richard, et al. “Localization for Transversally Periodic Random Potentials on Binary Trees.” Journal of Spectral Theory, vol. 6, no. 3, European Mathematical Society, 2016, pp. 557–600, doi:10.4171/JST/132.","ista":"Froese R, Lee D, Sadel C, Spitzer W, Stolz G. 2016. Localization for transversally periodic random potentials on binary trees. Journal of Spectral Theory. 6(3), 557–600.","chicago":"Froese, Richard, Darrick Lee, Christian Sadel, Wolfgang Spitzer, and Günter Stolz. “Localization for Transversally Periodic Random Potentials on Binary Trees.” Journal of Spectral Theory. European Mathematical Society, 2016. https://doi.org/10.4171/JST/132."},"month":"01","intvolume":" 6","scopus_import":1,"quality_controlled":"1","publisher":"European Mathematical Society","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1408.3961","open_access":"1"}],"oa_version":"Preprint","abstract":[{"text":"We consider a random Schrödinger operator on the binary tree with a random potential which is the sum of a random radially symmetric potential, Qr, and a random transversally periodic potential, κQt, with coupling constant κ. Using a new one-dimensional dynamical systems approach combined with Jensen's inequality in hyperbolic space (our key estimate) we obtain a fractional moment estimate proving localization for small and large κ. Together with a previous result we therefore obtain a model with two Anderson transitions, from localization to delocalization and back to localization, when increasing κ. As a by-product we also have a partially new proof of one-dimensional Anderson localization at any disorder.","lang":"eng"}],"issue":"3","doi":"10.4171/JST/132","volume":6,"date_published":"2016-01-01T00:00:00Z","date_created":"2018-12-11T11:50:48Z","page":"557 - 600","day":"01","language":[{"iso":"eng"}],"publication":"Journal of Spectral Theory","year":"2016","publication_status":"published"},{"type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","pubrep_id":"703","_id":"1257","file_date_updated":"2020-07-14T12:44:42Z","department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T06:49:26Z","ddc":["510","539"],"scopus_import":1,"month":"05","intvolume":" 343","abstract":[{"lang":"eng","text":"We consider products of random matrices that are small, independent identically distributed perturbations of a fixed matrix (Formula presented.). Focusing on the eigenvalues of (Formula presented.) of a particular size we obtain a limit to a SDE in a critical scaling. Previous results required (Formula presented.) to be a (conjugated) unitary matrix so it could not have eigenvalues of different modulus. From the result we can also obtain a limit SDE for the Markov process given by the action of the random products on the flag manifold. Applying the result to random Schrödinger operators we can improve some results by Valko and Virag showing GOE statistics for the rescaled eigenvalue process of a sequence of Anderson models on long boxes. In particular, we solve a problem posed in their work."}],"oa_version":"Published Version","issue":"3","volume":343,"ec_funded":1,"publication_status":"published","file":[{"checksum":"4fb2411d9c2f56676123165aad46c828","file_id":"5119","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2018-12-12T10:15:02Z","file_name":"IST-2016-703-v1+1_s00220-016-2600-4.pdf","date_updated":"2020-07-14T12:44:42Z","file_size":800792,"creator":"system"}],"language":[{"iso":"eng"}],"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publist_id":"6067","author":[{"full_name":"Sadel, Christian","orcid":"0000-0001-8255-3968","last_name":"Sadel","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","first_name":"Christian"},{"first_name":"Bálint","last_name":"Virág","full_name":"Virág, Bálint"}],"article_processing_charge":"Yes (via OA deal)","title":"A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes","citation":{"ieee":"C. Sadel and B. Virág, “A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes,” Communications in Mathematical Physics, vol. 343, no. 3. Springer, pp. 881–919, 2016.","short":"C. Sadel, B. Virág, Communications in Mathematical Physics 343 (2016) 881–919.","apa":"Sadel, C., & Virág, B. (2016). A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-016-2600-4","ama":"Sadel C, Virág B. A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. Communications in Mathematical Physics. 2016;343(3):881-919. doi:10.1007/s00220-016-2600-4","mla":"Sadel, Christian, and Bálint Virág. “A Central Limit Theorem for Products of Random Matrices and GOE Statistics for the Anderson Model on Long Boxes.” Communications in Mathematical Physics, vol. 343, no. 3, Springer, 2016, pp. 881–919, doi:10.1007/s00220-016-2600-4.","ista":"Sadel C, Virág B. 2016. A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes. Communications in Mathematical Physics. 343(3), 881–919.","chicago":"Sadel, Christian, and Bálint Virág. “A Central Limit Theorem for Products of Random Matrices and GOE Statistics for the Anderson Model on Long Boxes.” Communications in Mathematical Physics. Springer, 2016. https://doi.org/10.1007/s00220-016-2600-4."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publisher":"Springer","quality_controlled":"1","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The work of C. Sadel was supported by NSERC Discovery Grant 92997-2010 RGPIN and by the People Programme (Marie Curie Actions) of the EU 7th Framework Programme FP7/2007-2013, REA Grant 291734.","page":"881 - 919","doi":"10.1007/s00220-016-2600-4","date_published":"2016-05-01T00:00:00Z","date_created":"2018-12-11T11:50:59Z","has_accepted_license":"1","year":"2016","day":"01","publication":"Communications in Mathematical Physics"},{"intvolume":" 69","month":"10","main_file_link":[{"url":"https://arxiv.org/abs/1407.5606","open_access":"1"}],"scopus_import":1,"oa_version":"Preprint","abstract":[{"text":"We prove the Wigner-Dyson-Mehta conjecture at fixed energy in the bulk of the spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results concerning the universality of random matrices either require an averaging in the energy parameter or they hold only for Hermitian matrices if the energy parameter is fixed. We develop a homogenization theory of the Dyson Brownian motion and show that microscopic universality follows from mesoscopic statistics.","lang":"eng"}],"ec_funded":1,"volume":69,"issue":"10","language":[{"iso":"eng"}],"publication_status":"published","status":"public","type":"journal_article","_id":"1280","department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T06:49:35Z","oa":1,"publisher":"Wiley-Blackwell","acknowledgement":"The work of P.B. was partially supported by National Sci-\r\nence Foundation Grant DMS-1208859. The work of L.E. was partially supported\r\nby ERC Advanced Grant RANMAT 338804. The work of H.-T. Y. was partially\r\nsupported by National Science Foundation Grant DMS-1307444 and a Simons In-\r\nvestigator award. The work of J.Y. was partially supported by National Science\r\nFoundation Grant DMS-1207961. The major part of this research was conducted\r\nwhen all authors were visiting IAS and were also supported by National Science\r\nFoundation Grant DMS-1128255.","date_created":"2018-12-11T11:51:07Z","date_published":"2016-10-01T00:00:00Z","doi":"10.1002/cpa.21624","page":"1815 - 1881","publication":"Communications on Pure and Applied Mathematics","day":"01","year":"2016","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"title":"Fixed energy universality for generalized wigner matrices","author":[{"full_name":"Bourgade, Paul","last_name":"Bourgade","first_name":"Paul"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Yau","full_name":"Yau, Horngtzer","first_name":"Horngtzer"},{"first_name":"Jun","last_name":"Yin","full_name":"Yin, Jun"}],"publist_id":"6036","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Bourgade, P., Erdös, L., Yau, H., & Yin, J. (2016). Fixed energy universality for generalized wigner matrices. Communications on Pure and Applied Mathematics. Wiley-Blackwell. https://doi.org/10.1002/cpa.21624","ama":"Bourgade P, Erdös L, Yau H, Yin J. Fixed energy universality for generalized wigner matrices. Communications on Pure and Applied Mathematics. 2016;69(10):1815-1881. doi:10.1002/cpa.21624","ieee":"P. Bourgade, L. Erdös, H. Yau, and J. Yin, “Fixed energy universality for generalized wigner matrices,” Communications on Pure and Applied Mathematics, vol. 69, no. 10. Wiley-Blackwell, pp. 1815–1881, 2016.","short":"P. Bourgade, L. Erdös, H. Yau, J. Yin, Communications on Pure and Applied Mathematics 69 (2016) 1815–1881.","mla":"Bourgade, Paul, et al. “Fixed Energy Universality for Generalized Wigner Matrices.” Communications on Pure and Applied Mathematics, vol. 69, no. 10, Wiley-Blackwell, 2016, pp. 1815–81, doi:10.1002/cpa.21624.","ista":"Bourgade P, Erdös L, Yau H, Yin J. 2016. Fixed energy universality for generalized wigner matrices. Communications on Pure and Applied Mathematics. 69(10), 1815–1881.","chicago":"Bourgade, Paul, László Erdös, Horngtzer Yau, and Jun Yin. “Fixed Energy Universality for Generalized Wigner Matrices.” Communications on Pure and Applied Mathematics. Wiley-Blackwell, 2016. https://doi.org/10.1002/cpa.21624."}},{"day":"01","publication":"Journal of Functional Analysis","year":"2016","doi":"10.1016/j.jfa.2016.04.006","date_published":"2016-08-01T00:00:00Z","date_created":"2018-12-11T11:52:00Z","page":"672 - 719","publisher":"Academic Press","quality_controlled":"1","oa":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Bao Z, Erdös L, Schnelli K. 2016. Local stability of the free additive convolution. Journal of Functional Analysis. 271(3), 672–719.","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Local Stability of the Free Additive Convolution.” Journal of Functional Analysis. Academic Press, 2016. https://doi.org/10.1016/j.jfa.2016.04.006.","apa":"Bao, Z., Erdös, L., & Schnelli, K. (2016). Local stability of the free additive convolution. Journal of Functional Analysis. Academic Press. https://doi.org/10.1016/j.jfa.2016.04.006","ama":"Bao Z, Erdös L, Schnelli K. Local stability of the free additive convolution. Journal of Functional Analysis. 2016;271(3):672-719. doi:10.1016/j.jfa.2016.04.006","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Local stability of the free additive convolution,” Journal of Functional Analysis, vol. 271, no. 3. Academic Press, pp. 672–719, 2016.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 271 (2016) 672–719.","mla":"Bao, Zhigang, et al. “Local Stability of the Free Additive Convolution.” Journal of Functional Analysis, vol. 271, no. 3, Academic Press, 2016, pp. 672–719, doi:10.1016/j.jfa.2016.04.006."},"title":"Local stability of the free additive convolution","author":[{"full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","last_name":"Schnelli"}],"publist_id":"5764","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"language":[{"iso":"eng"}],"publication_status":"published","issue":"3","volume":271,"ec_funded":1,"oa_version":"Preprint","abstract":[{"text":"We prove that the system of subordination equations, defining the free additive convolution of two probability measures, is stable away from the edges of the support and blow-up singularities by showing that the recent smoothness condition of Kargin is always satisfied. As an application, we consider the local spectral statistics of the random matrix ensemble A+UBU⁎A+UBU⁎, where U is a Haar distributed random unitary or orthogonal matrix, and A and B are deterministic matrices. In the bulk regime, we prove that the empirical spectral distribution of A+UBU⁎A+UBU⁎ concentrates around the free additive convolution of the spectral distributions of A and B on scales down to N−2/3N−2/3.","lang":"eng"}],"month":"08","intvolume":" 271","scopus_import":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1508.05905"}],"date_updated":"2021-01-12T06:50:42Z","department":[{"_id":"LaEr"}],"_id":"1434","status":"public","type":"journal_article"},{"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"title":"Local spectral statistics of Gaussian matrices with correlated entries","author":[{"first_name":"Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","last_name":"Ajanki","full_name":"Ajanki, Oskari H"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"5698","article_processing_charge":"Yes (via OA deal)","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Local Spectral Statistics of Gaussian Matrices with Correlated Entries.” Journal of Statistical Physics. Springer, 2016. https://doi.org/10.1007/s10955-016-1479-y.","ista":"Ajanki OH, Erdös L, Krüger TH. 2016. Local spectral statistics of Gaussian matrices with correlated entries. Journal of Statistical Physics. 163(2), 280–302.","mla":"Ajanki, Oskari H., et al. “Local Spectral Statistics of Gaussian Matrices with Correlated Entries.” Journal of Statistical Physics, vol. 163, no. 2, Springer, 2016, pp. 280–302, doi:10.1007/s10955-016-1479-y.","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local spectral statistics of Gaussian matrices with correlated entries,” Journal of Statistical Physics, vol. 163, no. 2. Springer, pp. 280–302, 2016.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Journal of Statistical Physics 163 (2016) 280–302.","ama":"Ajanki OH, Erdös L, Krüger TH. Local spectral statistics of Gaussian matrices with correlated entries. Journal of Statistical Physics. 2016;163(2):280-302. doi:10.1007/s10955-016-1479-y","apa":"Ajanki, O. H., Erdös, L., & Krüger, T. H. (2016). Local spectral statistics of Gaussian matrices with correlated entries. Journal of Statistical Physics. Springer. https://doi.org/10.1007/s10955-016-1479-y"},"quality_controlled":"1","publisher":"Springer","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Oskari H. Ajanki was Partially supported by ERC Advanced Grant RANMAT No. 338804, and SFB-TR 12 Grant of the German Research Council. László Erdős was Partially supported by ERC Advanced Grant RANMAT No. 338804. Torben Krüger was Partially supported by ERC Advanced Grant RANMAT No. 338804, and SFB-TR 12 Grant of the German Research Council.","doi":"10.1007/s10955-016-1479-y","date_published":"2016-04-01T00:00:00Z","date_created":"2018-12-11T11:52:19Z","page":"280 - 302","day":"01","publication":"Journal of Statistical Physics","has_accepted_license":"1","year":"2016","status":"public","pubrep_id":"516","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"_id":"1489","file_date_updated":"2020-07-14T12:44:57Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2021-01-12T06:51:05Z","month":"04","intvolume":" 163","scopus_import":1,"oa_version":"Published Version","abstract":[{"text":"We prove optimal local law, bulk universality and non-trivial decay for the off-diagonal elements of the resolvent for a class of translation invariant Gaussian random matrix ensembles with correlated entries. ","lang":"eng"}],"issue":"2","volume":163,"ec_funded":1,"file":[{"date_created":"2018-12-12T10:11:16Z","file_name":"IST-2016-516-v1+1_s10955-016-1479-y.pdf","date_updated":"2020-07-14T12:44:57Z","file_size":660602,"creator":"system","checksum":"7139598dcb1cafbe6866bd2bfd732b33","file_id":"4869","content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"publication_status":"published"},{"ec_funded":1,"volume":17,"issue":"7","language":[{"iso":"eng"}],"publication_status":"published","intvolume":" 17","month":"07","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1501.04287"}],"scopus_import":1,"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We show that the Anderson model has a transition from localization to delocalization at exactly 2 dimensional growth rate on antitrees with normalized edge weights which are certain discrete graphs. The kinetic part has a one-dimensional structure allowing a description through transfer matrices which involve some Schur complement. For such operators we introduce the notion of having one propagating channel and extend theorems from the theory of one-dimensional Jacobi operators that relate the behavior of transfer matrices with the spectrum. These theorems are then applied to the considered model. In essence, in a certain energy region the kinetic part averages the random potentials along shells and the transfer matrices behave similar as for a one-dimensional operator with random potential of decaying variance. At d dimensional growth for d>2 this effective decay is strong enough to obtain absolutely continuous spectrum, whereas for some uniform d dimensional growth with d<2 one has pure point spectrum in this energy region. At exactly uniform 2 dimensional growth also some singular continuous spectrum appears, at least at small disorder. As a corollary we also obtain a change from singular spectrum (d≤2) to absolutely continuous spectrum (d≥3) for random operators of the type rΔdr+λ on ℤd, where r is an orthogonal radial projection, Δd the discrete adjacency operator (Laplacian) on ℤd and λ a random potential. "}],"department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T06:51:58Z","status":"public","type":"journal_article","_id":"1608","date_created":"2018-12-11T11:53:00Z","date_published":"2016-07-01T00:00:00Z","doi":"10.1007/s00023-015-0456-3","page":"1631 - 1675","publication":"Annales Henri Poincare","day":"01","year":"2016","oa":1,"quality_controlled":"1","publisher":"Birkhäuser","title":"Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel","publist_id":"5558","author":[{"id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","first_name":"Christian","last_name":"Sadel","full_name":"Sadel, Christian","orcid":"0000-0001-8255-3968"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ama":"Sadel C. Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel. Annales Henri Poincare. 2016;17(7):1631-1675. doi:10.1007/s00023-015-0456-3","apa":"Sadel, C. (2016). Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel. Annales Henri Poincare. Birkhäuser. https://doi.org/10.1007/s00023-015-0456-3","ieee":"C. Sadel, “Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel,” Annales Henri Poincare, vol. 17, no. 7. Birkhäuser, pp. 1631–1675, 2016.","short":"C. Sadel, Annales Henri Poincare 17 (2016) 1631–1675.","mla":"Sadel, Christian. “Anderson Transition at 2 Dimensional Growth Rate on Antitrees and Spectral Theory for Operators with One Propagating Channel.” Annales Henri Poincare, vol. 17, no. 7, Birkhäuser, 2016, pp. 1631–75, doi:10.1007/s00023-015-0456-3.","ista":"Sadel C. 2016. Anderson transition at 2 dimensional growth rate on antitrees and spectral theory for operators with one propagating channel. Annales Henri Poincare. 17(7), 1631–1675.","chicago":"Sadel, Christian. “Anderson Transition at 2 Dimensional Growth Rate on Antitrees and Spectral Theory for Operators with One Propagating Channel.” Annales Henri Poincare. Birkhäuser, 2016. https://doi.org/10.1007/s00023-015-0456-3."},"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}]},{"date_updated":"2021-01-12T06:53:49Z","department":[{"_id":"LaEr"}],"_id":"1881","type":"journal_article","status":"public","publication_status":"published","language":[{"iso":"eng"}],"ec_funded":1,"issue":"1-2","volume":164,"abstract":[{"text":"We consider random matrices of the form H=W+λV, λ∈ℝ+, where W is a real symmetric or complex Hermitian Wigner matrix of size N and V is a real bounded diagonal random matrix of size N with i.i.d.\\ entries that are independent of W. We assume subexponential decay for the matrix entries of W and we choose λ∼1, so that the eigenvalues of W and λV are typically of the same order. Further, we assume that the density of the entries of V is supported on a single interval and is convex near the edges of its support. In this paper we prove that there is λ+∈ℝ+ such that the largest eigenvalues of H are in the limit of large N determined by the order statistics of V for λ>λ+. In particular, the largest eigenvalue of H has a Weibull distribution in the limit N→∞ if λ>λ+. Moreover, for N sufficiently large, we show that the eigenvectors associated to the largest eigenvalues are partially localized for λ>λ+, while they are completely delocalized for λ<λ+. Similar results hold for the lowest eigenvalues. ","lang":"eng"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1310.7057"}],"scopus_import":1,"intvolume":" 164","month":"02","citation":{"chicago":"Lee, Jioon, and Kevin Schnelli. “Extremal Eigenvalues and Eigenvectors of Deformed Wigner Matrices.” Probability Theory and Related Fields. Springer, 2016. https://doi.org/10.1007/s00440-014-0610-8.","ista":"Lee J, Schnelli K. 2016. Extremal eigenvalues and eigenvectors of deformed Wigner matrices. Probability Theory and Related Fields. 164(1–2), 165–241.","mla":"Lee, Jioon, and Kevin Schnelli. “Extremal Eigenvalues and Eigenvectors of Deformed Wigner Matrices.” Probability Theory and Related Fields, vol. 164, no. 1–2, Springer, 2016, pp. 165–241, doi:10.1007/s00440-014-0610-8.","ieee":"J. Lee and K. Schnelli, “Extremal eigenvalues and eigenvectors of deformed Wigner matrices,” Probability Theory and Related Fields, vol. 164, no. 1–2. Springer, pp. 165–241, 2016.","short":"J. Lee, K. Schnelli, Probability Theory and Related Fields 164 (2016) 165–241.","apa":"Lee, J., & Schnelli, K. (2016). Extremal eigenvalues and eigenvectors of deformed Wigner matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-014-0610-8","ama":"Lee J, Schnelli K. Extremal eigenvalues and eigenvectors of deformed Wigner matrices. Probability Theory and Related Fields. 2016;164(1-2):165-241. doi:10.1007/s00440-014-0610-8"},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publist_id":"5215","author":[{"full_name":"Lee, Jioon","last_name":"Lee","first_name":"Jioon"},{"orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"}],"title":"Extremal eigenvalues and eigenvectors of deformed Wigner matrices","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"year":"2016","publication":"Probability Theory and Related Fields","day":"01","page":"165 - 241","date_created":"2018-12-11T11:54:31Z","date_published":"2016-02-01T00:00:00Z","doi":"10.1007/s00440-014-0610-8","acknowledgement":"Most of the presented work was obtained while Kevin Schnelli was staying at the IAS with the support of\r\nThe Fund For Math.","oa":1,"publisher":"Springer","quality_controlled":"1"},{"_id":"1505","status":"public","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:51:14Z","citation":{"ista":"Bao Z, Pan G, Zhou W. 2015. Universality for the largest eigenvalue of sample covariance matrices with general population. Annals of Statistics. 43(1), 382–421.","chicago":"Bao, Zhigang, Guangming Pan, and Wang Zhou. “Universality for the Largest Eigenvalue of Sample Covariance Matrices with General Population.” Annals of Statistics. Institute of Mathematical Statistics, 2015. https://doi.org/10.1214/14-AOS1281.","ieee":"Z. Bao, G. Pan, and W. Zhou, “Universality for the largest eigenvalue of sample covariance matrices with general population,” Annals of Statistics, vol. 43, no. 1. Institute of Mathematical Statistics, pp. 382–421, 2015.","short":"Z. Bao, G. Pan, W. Zhou, Annals of Statistics 43 (2015) 382–421.","apa":"Bao, Z., Pan, G., & Zhou, W. (2015). Universality for the largest eigenvalue of sample covariance matrices with general population. Annals of Statistics. Institute of Mathematical Statistics. https://doi.org/10.1214/14-AOS1281","ama":"Bao Z, Pan G, Zhou W. Universality for the largest eigenvalue of sample covariance matrices with general population. Annals of Statistics. 2015;43(1):382-421. doi:10.1214/14-AOS1281","mla":"Bao, Zhigang, et al. “Universality for the Largest Eigenvalue of Sample Covariance Matrices with General Population.” Annals of Statistics, vol. 43, no. 1, Institute of Mathematical Statistics, 2015, pp. 382–421, doi:10.1214/14-AOS1281."},"department":[{"_id":"LaEr"}],"title":"Universality for the largest eigenvalue of sample covariance matrices with general population","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang","last_name":"Bao","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang"},{"last_name":"Pan","full_name":"Pan, Guangming","first_name":"Guangming"},{"first_name":"Wang","full_name":"Zhou, Wang","last_name":"Zhou"}],"publist_id":"5672","oa_version":"Preprint","acknowledgement":"B.Z. was supported in part by NSFC Grant 11071213, ZJNSF Grant R6090034 and SRFDP Grant 20100101110001. P.G. was supported in part by the Ministry of Education, Singapore, under Grant ARC 14/11. Z.W. was supported in part by the Ministry of Education, Singapore, under Grant ARC 14/11, and by a Grant R-155-000-131-112 at the National University of Singapore\r\n","abstract":[{"lang":"eng","text":"This paper is aimed at deriving the universality of the largest eigenvalue of a class of high-dimensional real or complex sample covariance matrices of the form W N =Σ 1/2XX∗Σ 1/2 . Here, X = (xij )M,N is an M× N random matrix with independent entries xij , 1 ≤ i M,≤ 1 ≤ j ≤ N such that Exij = 0, E|xij |2 = 1/N . On dimensionality, we assume that M = M(N) and N/M → d ε (0, ∞) as N ∞→. For a class of general deterministic positive-definite M × M matrices Σ , under some additional assumptions on the distribution of xij 's, we show that the limiting behavior of the largest eigenvalue of W N is universal, via pursuing a Green function comparison strategy raised in [Probab. Theory Related Fields 154 (2012) 341-407, Adv. Math. 229 (2012) 1435-1515] by Erd″os, Yau and Yin for Wigner matrices and extended by Pillai and Yin [Ann. Appl. Probab. 24 (2014) 935-1001] to sample covariance matrices in the null case (&Epsi = I ). Consequently, in the standard complex case (Ex2 ij = 0), combing this universality property and the results known for Gaussian matrices obtained by El Karoui in [Ann. Probab. 35 (2007) 663-714] (nonsingular case) and Onatski in [Ann. Appl. Probab. 18 (2008) 470-490] (singular case), we show that after an appropriate normalization the largest eigenvalue of W N converges weakly to the type 2 Tracy-Widom distribution TW2 . Moreover, in the real case, we show that whenΣ is spiked with a fixed number of subcritical spikes, the type 1 Tracy-Widom limit TW1 holds for the normalized largest eigenvalue of W N , which extends a result of Féral and Péché in [J. Math. Phys. 50 (2009) 073302] to the scenario of nondiagonal Σ and more generally distributed X . In summary, we establish the Tracy-Widom type universality for the largest eigenvalue of generally distributed sample covariance matrices under quite light assumptions on &Sigma . Applications of these limiting results to statistical signal detection and structure recognition of separable covariance matrices are also discussed."}],"month":"02","intvolume":" 43","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1304.5690"}],"day":"01","language":[{"iso":"eng"}],"publication":"Annals of Statistics","publication_status":"published","year":"2015","issue":"1","volume":43,"doi":"10.1214/14-AOS1281","date_published":"2015-02-01T00:00:00Z","date_created":"2018-12-11T11:52:25Z","page":"382 - 421"},{"title":"Gap universality of generalized Wigner and β ensembles","department":[{"_id":"LaEr"}],"author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"full_name":"Yau, Horng","last_name":"Yau","first_name":"Horng"}],"publist_id":"5669","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"L. Erdös, H. Yau, Journal of the European Mathematical Society 17 (2015) 1927–2036.","ieee":"L. Erdös and H. Yau, “Gap universality of generalized Wigner and β ensembles,” Journal of the European Mathematical Society, vol. 17, no. 8. European Mathematical Society, pp. 1927–2036, 2015.","ama":"Erdös L, Yau H. Gap universality of generalized Wigner and β ensembles. Journal of the European Mathematical Society. 2015;17(8):1927-2036. doi:10.4171/JEMS/548","apa":"Erdös, L., & Yau, H. (2015). Gap universality of generalized Wigner and β ensembles. Journal of the European Mathematical Society. European Mathematical Society. https://doi.org/10.4171/JEMS/548","mla":"Erdös, László, and Horng Yau. “Gap Universality of Generalized Wigner and β Ensembles.” Journal of the European Mathematical Society, vol. 17, no. 8, European Mathematical Society, 2015, pp. 1927–2036, doi:10.4171/JEMS/548.","ista":"Erdös L, Yau H. 2015. Gap universality of generalized Wigner and β ensembles. Journal of the European Mathematical Society. 17(8), 1927–2036.","chicago":"Erdös, László, and Horng Yau. “Gap Universality of Generalized Wigner and β Ensembles.” Journal of the European Mathematical Society. European Mathematical Society, 2015. https://doi.org/10.4171/JEMS/548."},"date_updated":"2021-01-12T06:51:15Z","status":"public","type":"journal_article","_id":"1508","issue":"8","doi":"10.4171/JEMS/548","date_published":"2015-08-01T00:00:00Z","volume":17,"date_created":"2018-12-11T11:52:26Z","page":"1927 - 2036","day":"01","language":[{"iso":"eng"}],"publication":"Journal of the European Mathematical Society","publication_status":"published","year":"2015","month":"08","intvolume":" 17","quality_controlled":"1","scopus_import":1,"publisher":"European Mathematical Society","oa":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1211.3786"}],"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We consider generalized Wigner ensembles and general β-ensembles with analytic potentials for any β ≥ 1. The recent universality results in particular assert that the local averages of consecutive eigenvalue gaps in the bulk of the spectrum are universal in the sense that they coincide with those of the corresponding Gaussian β-ensembles. In this article, we show that local averaging is not necessary for this result, i.e. we prove that the single gap distributions in the bulk are universal. In fact, with an additional step, our result can be extended to any C4(ℝ) potential."}]},{"department":[{"_id":"LaEr"}],"title":"The logarithmic law of random determinant","publist_id":"5671","author":[{"last_name":"Bao","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Guangming","full_name":"Pan, Guangming","last_name":"Pan"},{"first_name":"Wang","full_name":"Zhou, Wang","last_name":"Zhou"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"short":"Z. Bao, G. Pan, W. Zhou, Bernoulli 21 (2015) 1600–1628.","ieee":"Z. Bao, G. Pan, and W. Zhou, “The logarithmic law of random determinant,” Bernoulli, vol. 21, no. 3. Bernoulli Society for Mathematical Statistics and Probability, pp. 1600–1628, 2015.","ama":"Bao Z, Pan G, Zhou W. The logarithmic law of random determinant. Bernoulli. 2015;21(3):1600-1628. doi:10.3150/14-BEJ615","apa":"Bao, Z., Pan, G., & Zhou, W. (2015). The logarithmic law of random determinant. Bernoulli. Bernoulli Society for Mathematical Statistics and Probability. https://doi.org/10.3150/14-BEJ615","mla":"Bao, Zhigang, et al. “The Logarithmic Law of Random Determinant.” Bernoulli, vol. 21, no. 3, Bernoulli Society for Mathematical Statistics and Probability, 2015, pp. 1600–28, doi:10.3150/14-BEJ615.","ista":"Bao Z, Pan G, Zhou W. 2015. The logarithmic law of random determinant. Bernoulli. 21(3), 1600–1628.","chicago":"Bao, Zhigang, Guangming Pan, and Wang Zhou. “The Logarithmic Law of Random Determinant.” Bernoulli. Bernoulli Society for Mathematical Statistics and Probability, 2015. https://doi.org/10.3150/14-BEJ615."},"date_updated":"2021-01-12T06:51:14Z","status":"public","type":"journal_article","_id":"1506","date_created":"2018-12-11T11:52:25Z","date_published":"2015-08-01T00:00:00Z","doi":"10.3150/14-BEJ615","volume":21,"issue":"3","page":"1600 - 1628","language":[{"iso":"eng"}],"publication":"Bernoulli","day":"01","publication_status":"published","year":"2015","intvolume":" 21","month":"08","main_file_link":[{"url":"http://arxiv.org/abs/1208.5823","open_access":"1"}],"oa":1,"publisher":"Bernoulli Society for Mathematical Statistics and Probability","quality_controlled":"1","oa_version":"Preprint","abstract":[{"lang":"eng","text":"Consider the square random matrix An = (aij)n,n, where {aij:= a(n)ij , i, j = 1, . . . , n} is a collection of independent real random variables with means zero and variances one. Under the additional moment condition supn max1≤i,j ≤n Ea4ij <∞, we prove Girko's logarithmic law of det An in the sense that as n→∞ log | detAn| ? (1/2) log(n-1)! d/→√(1/2) log n N(0, 1)."}]},{"scopus_import":1,"publisher":"IEEE","quality_controlled":"1","month":"06","intvolume":" 61","abstract":[{"lang":"eng","text":"In this paper, we consider the fluctuation of mutual information statistics of a multiple input multiple output channel communication systems without assuming that the entries of the channel matrix have zero pseudovariance. To this end, we also establish a central limit theorem of the linear spectral statistics for sample covariance matrices under general moment conditions by removing the restrictions imposed on the second moment and fourth moment on the matrix entries in Bai and Silverstein (2004)."}],"oa_version":"None","acknowledgement":"G. Pan was supported by MOE Tier 2 under Grant 2014-T2-2-060 and in part by Tier 1 under Grant RG25/14 through the Nanyang Technological University, Singapore. W. Zhou was supported by the National University of Singapore, Singapore, under Grant R-155-000-131-112.\r\n","page":"3413 - 3426","date_published":"2015-06-01T00:00:00Z","issue":"6","doi":"10.1109/TIT.2015.2421894","volume":61,"date_created":"2018-12-11T11:52:52Z","publication_status":"published","year":"2015","day":"01","language":[{"iso":"eng"}],"publication":"IEEE Transactions on Information Theory","type":"journal_article","status":"public","_id":"1585","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang","last_name":"Bao","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475"},{"full_name":"Pan, Guangming","last_name":"Pan","first_name":"Guangming"},{"full_name":"Zhou, Wang","last_name":"Zhou","first_name":"Wang"}],"publist_id":"5586","department":[{"_id":"LaEr"}],"title":"Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices","date_updated":"2021-01-12T06:51:46Z","citation":{"mla":"Bao, Zhigang, et al. “Asymptotic Mutual Information Statistics of MIMO Channels and CLT of Sample Covariance Matrices.” IEEE Transactions on Information Theory, vol. 61, no. 6, IEEE, 2015, pp. 3413–26, doi:10.1109/TIT.2015.2421894.","ieee":"Z. Bao, G. Pan, and W. Zhou, “Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices,” IEEE Transactions on Information Theory, vol. 61, no. 6. IEEE, pp. 3413–3426, 2015.","short":"Z. Bao, G. Pan, W. Zhou, IEEE Transactions on Information Theory 61 (2015) 3413–3426.","ama":"Bao Z, Pan G, Zhou W. Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices. IEEE Transactions on Information Theory. 2015;61(6):3413-3426. doi:10.1109/TIT.2015.2421894","apa":"Bao, Z., Pan, G., & Zhou, W. (2015). Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices. IEEE Transactions on Information Theory. IEEE. https://doi.org/10.1109/TIT.2015.2421894","chicago":"Bao, Zhigang, Guangming Pan, and Wang Zhou. “Asymptotic Mutual Information Statistics of MIMO Channels and CLT of Sample Covariance Matrices.” IEEE Transactions on Information Theory. IEEE, 2015. https://doi.org/10.1109/TIT.2015.2421894.","ista":"Bao Z, Pan G, Zhou W. 2015. Asymptotic mutual information statistics of MIMO channels and CLT of sample covariance matrices. IEEE Transactions on Information Theory. 61(6), 3413–3426."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"department":[{"_id":"LaEr"}],"title":"Edge universality for deformed Wigner matrices","publist_id":"5475","author":[{"first_name":"Jioon","last_name":"Lee","full_name":"Lee, Jioon"},{"last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"chicago":"Lee, Jioon, and Kevin Schnelli. “Edge Universality for Deformed Wigner Matrices.” Reviews in Mathematical Physics. World Scientific Publishing, 2015. https://doi.org/10.1142/S0129055X1550018X.","ista":"Lee J, Schnelli K. 2015. Edge universality for deformed Wigner matrices. Reviews in Mathematical Physics. 27(8), 1550018.","mla":"Lee, Jioon, and Kevin Schnelli. “Edge Universality for Deformed Wigner Matrices.” Reviews in Mathematical Physics, vol. 27, no. 8, 1550018, World Scientific Publishing, 2015, doi:10.1142/S0129055X1550018X.","ama":"Lee J, Schnelli K. Edge universality for deformed Wigner matrices. Reviews in Mathematical Physics. 2015;27(8). doi:10.1142/S0129055X1550018X","apa":"Lee, J., & Schnelli, K. (2015). Edge universality for deformed Wigner matrices. Reviews in Mathematical Physics. World Scientific Publishing. https://doi.org/10.1142/S0129055X1550018X","ieee":"J. Lee and K. Schnelli, “Edge universality for deformed Wigner matrices,” Reviews in Mathematical Physics, vol. 27, no. 8. World Scientific Publishing, 2015.","short":"J. Lee, K. Schnelli, Reviews in Mathematical Physics 27 (2015)."},"date_updated":"2021-01-12T06:52:26Z","status":"public","type":"journal_article","article_number":"1550018","_id":"1674","date_created":"2018-12-11T11:53:24Z","doi":"10.1142/S0129055X1550018X","date_published":"2015-09-01T00:00:00Z","volume":27,"issue":"8","language":[{"iso":"eng"}],"publication":"Reviews in Mathematical Physics","day":"01","publication_status":"published","year":"2015","intvolume":" 27","month":"09","oa":1,"main_file_link":[{"url":"http://arxiv.org/abs/1407.8015","open_access":"1"}],"quality_controlled":"1","scopus_import":1,"publisher":"World Scientific Publishing","oa_version":"Preprint","abstract":[{"text":"We consider N × N random matrices of the form H = W + V where W is a real symmetric Wigner matrix and V a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W and we choose V so that the eigenvalues of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the rescaled distribution of the extremal eigenvalues is given by the Tracy-Widom distribution F1 in the limit of large N. Our proofs also apply to the complex Hermitian setting, i.e. when W is a complex Hermitian Wigner matrix.","lang":"eng"}]},{"article_number":"6977","author":[{"first_name":"Johannes","full_name":"Knebel, Johannes","last_name":"Knebel"},{"first_name":"Markus","last_name":"Weber","full_name":"Weber, Markus"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger"},{"last_name":"Frey","full_name":"Frey, Erwin","first_name":"Erwin"}],"publist_id":"5282","title":"Evolutionary games of condensates in coupled birth-death processes","citation":{"mla":"Knebel, Johannes, et al. “Evolutionary Games of Condensates in Coupled Birth-Death Processes.” Nature Communications, vol. 6, 6977, Nature Publishing Group, 2015, doi:10.1038/ncomms7977.","apa":"Knebel, J., Weber, M., Krüger, T. H., & Frey, E. (2015). Evolutionary games of condensates in coupled birth-death processes. Nature Communications. Nature Publishing Group. https://doi.org/10.1038/ncomms7977","ama":"Knebel J, Weber M, Krüger TH, Frey E. Evolutionary games of condensates in coupled birth-death processes. Nature Communications. 2015;6. doi:10.1038/ncomms7977","ieee":"J. Knebel, M. Weber, T. H. Krüger, and E. Frey, “Evolutionary games of condensates in coupled birth-death processes,” Nature Communications, vol. 6. Nature Publishing Group, 2015.","short":"J. Knebel, M. Weber, T.H. Krüger, E. Frey, Nature Communications 6 (2015).","chicago":"Knebel, Johannes, Markus Weber, Torben H Krüger, and Erwin Frey. “Evolutionary Games of Condensates in Coupled Birth-Death Processes.” Nature Communications. Nature Publishing Group, 2015. https://doi.org/10.1038/ncomms7977.","ista":"Knebel J, Weber M, Krüger TH, Frey E. 2015. Evolutionary games of condensates in coupled birth-death processes. Nature Communications. 6, 6977."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Nature Publishing Group","quality_controlled":"1","oa":1,"doi":"10.1038/ncomms7977","date_published":"2015-04-24T00:00:00Z","date_created":"2018-12-11T11:54:13Z","has_accepted_license":"1","year":"2015","day":"24","publication":"Nature Communications","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","pubrep_id":"451","_id":"1824","file_date_updated":"2020-07-14T12:45:17Z","department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T06:53:26Z","ddc":["530"],"scopus_import":1,"month":"04","intvolume":" 6","abstract":[{"text":"Condensation phenomena arise through a collective behaviour of particles. They are observed in both classical and quantum systems, ranging from the formation of traffic jams in mass transport models to the macroscopic occupation of the energetic ground state in ultra-cold bosonic gases (Bose-Einstein condensation). Recently, it has been shown that a driven and dissipative system of bosons may form multiple condensates. Which states become the condensates has, however, remained elusive thus far. The dynamics of this condensation are described by coupled birth-death processes, which also occur in evolutionary game theory. Here we apply concepts from evolutionary game theory to explain the formation of multiple condensates in such driven-dissipative bosonic systems. We show that the vanishing of relative entropy production determines their selection. The condensation proceeds exponentially fast, but the system never comes to rest. Instead, the occupation numbers of condensates may oscillate, as we demonstrate for a rock-paper-scissors game of condensates.","lang":"eng"}],"oa_version":"Published Version","volume":6,"publication_status":"published","file":[{"checksum":"c4cffb5c8b245e658a34eac71a03e7cc","file_id":"5245","access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2018-12-12T10:16:54Z","file_name":"IST-2016-451-v1+1_ncomms7977.pdf","creator":"system","date_updated":"2020-07-14T12:45:17Z","file_size":1151501}],"language":[{"iso":"eng"}]},{"ec_funded":1,"volume":16,"issue":"3","publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1309.5107"}],"scopus_import":1,"intvolume":" 16","month":"03","abstract":[{"lang":"eng","text":"The Altshuler–Shklovskii formulas (Altshuler and Shklovskii, BZh Eksp Teor Fiz 91:200, 1986) predict, for any disordered quantum system in the diffusive regime, a universal power law behaviour for the correlation functions of the mesoscopic eigenvalue density. In this paper and its companion (Erdős and Knowles, The Altshuler–Shklovskii formulas for random band matrices I: the unimodular case, 2013), we prove these formulas for random band matrices. In (Erdős and Knowles, The Altshuler–Shklovskii formulas for random band matrices I: the unimodular case, 2013) we introduced a diagrammatic approach and presented robust estimates on general diagrams under certain simplifying assumptions. In this paper, we remove these assumptions by giving a general estimate of the subleading diagrams. We also give a precise analysis of the leading diagrams which give rise to the Altschuler–Shklovskii power laws. Moreover, we introduce a family of general random band matrices which interpolates between real symmetric (β = 1) and complex Hermitian (β = 2) models, and track the transition for the mesoscopic density–density correlation. Finally, we address the higher-order correlation functions by proving that they behave asymptotically according to a Gaussian process whose covariance is given by the Altshuler–Shklovskii formulas.\r\n"}],"oa_version":"Preprint","department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T06:53:42Z","type":"journal_article","status":"public","_id":"1864","page":"709 - 799","date_created":"2018-12-11T11:54:26Z","date_published":"2015-03-01T00:00:00Z","doi":"10.1007/s00023-014-0333-5","year":"2015","publication":"Annales Henri Poincare","day":"01","oa":1,"publisher":"Springer","publist_id":"5233","author":[{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"last_name":"Knowles","full_name":"Knowles, Antti","first_name":"Antti"}],"title":"The Altshuler–Shklovskii formulas for random band matrices II: The general case","citation":{"chicago":"Erdös, László, and Antti Knowles. “The Altshuler–Shklovskii Formulas for Random Band Matrices II: The General Case.” Annales Henri Poincare. Springer, 2015. https://doi.org/10.1007/s00023-014-0333-5.","ista":"Erdös L, Knowles A. 2015. The Altshuler–Shklovskii formulas for random band matrices II: The general case. Annales Henri Poincare. 16(3), 709–799.","mla":"Erdös, László, and Antti Knowles. “The Altshuler–Shklovskii Formulas for Random Band Matrices II: The General Case.” Annales Henri Poincare, vol. 16, no. 3, Springer, 2015, pp. 709–99, doi:10.1007/s00023-014-0333-5.","short":"L. Erdös, A. Knowles, Annales Henri Poincare 16 (2015) 709–799.","ieee":"L. Erdös and A. Knowles, “The Altshuler–Shklovskii formulas for random band matrices II: The general case,” Annales Henri Poincare, vol. 16, no. 3. Springer, pp. 709–799, 2015.","apa":"Erdös, L., & Knowles, A. (2015). The Altshuler–Shklovskii formulas for random band matrices II: The general case. Annales Henri Poincare. Springer. https://doi.org/10.1007/s00023-014-0333-5","ama":"Erdös L, Knowles A. The Altshuler–Shklovskii formulas for random band matrices II: The general case. Annales Henri Poincare. 2015;16(3):709-799. doi:10.1007/s00023-014-0333-5"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}]},{"page":"1365 - 1416","date_created":"2018-12-11T11:56:05Z","issue":"3","date_published":"2015-02-01T00:00:00Z","volume":333,"doi":"10.1007/s00220-014-2119-5","year":"2015","publication_status":"published","language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","day":"01","main_file_link":[{"url":"http://arxiv.org/abs/1309.5106","open_access":"1"}],"oa":1,"scopus_import":1,"publisher":"Springer","quality_controlled":"1","intvolume":" 333","month":"02","abstract":[{"lang":"eng","text":"We consider the spectral statistics of large random band matrices on mesoscopic energy scales. We show that the correlation function of the local eigenvalue density exhibits a universal power law behaviour that differs from the Wigner-Dyson- Mehta statistics. This law had been predicted in the physics literature by Altshuler and Shklovskii in (Zh Eksp Teor Fiz (Sov Phys JETP) 91(64):220(127), 1986); it describes the correlations of the eigenvalue density in general metallic sampleswith weak disorder. Our result rigorously establishes the Altshuler-Shklovskii formulas for band matrices. In two dimensions, where the leading term vanishes owing to an algebraic cancellation, we identify the first non-vanishing term and show that it differs substantially from the prediction of Kravtsov and Lerner in (Phys Rev Lett 74:2563-2566, 1995). The proof is given in the current paper and its companion (Ann. H. Poincaré. arXiv:1309.5107, 2014). "}],"oa_version":"Preprint","publist_id":"4818","author":[{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Knowles, Antti","last_name":"Knowles","first_name":"Antti"}],"title":"The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case","department":[{"_id":"LaEr"}],"citation":{"ista":"Erdös L, Knowles A. 2015. The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case. Communications in Mathematical Physics. 333(3), 1365–1416.","chicago":"Erdös, László, and Antti Knowles. “The Altshuler-Shklovskii Formulas for Random Band Matrices I: The Unimodular Case.” Communications in Mathematical Physics. Springer, 2015. https://doi.org/10.1007/s00220-014-2119-5.","short":"L. Erdös, A. Knowles, Communications in Mathematical Physics 333 (2015) 1365–1416.","ieee":"L. Erdös and A. Knowles, “The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case,” Communications in Mathematical Physics, vol. 333, no. 3. Springer, pp. 1365–1416, 2015.","apa":"Erdös, L., & Knowles, A. (2015). The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-014-2119-5","ama":"Erdös L, Knowles A. The Altshuler-Shklovskii formulas for random band matrices I: the unimodular case. Communications in Mathematical Physics. 2015;333(3):1365-1416. doi:10.1007/s00220-014-2119-5","mla":"Erdös, László, and Antti Knowles. “The Altshuler-Shklovskii Formulas for Random Band Matrices I: The Unimodular Case.” Communications in Mathematical Physics, vol. 333, no. 3, Springer, 2015, pp. 1365–416, doi:10.1007/s00220-014-2119-5."},"date_updated":"2021-01-12T06:55:43Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article","status":"public","_id":"2166"},{"month":"10","intvolume":" 56","scopus_import":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1506.04683"}],"oa_version":"Preprint","abstract":[{"text":"We consider real symmetric and complex Hermitian random matrices with the additional symmetry hxy = hN-y,N-x. The matrix elements are independent (up to the fourfold symmetry) and not necessarily identically distributed. This ensemble naturally arises as the Fourier transform of a Gaussian orthogonal ensemble. Italso occurs as the flip matrix model - an approximation of the two-dimensional Anderson model at small disorder. We show that the density of states converges to the Wigner semicircle law despite the new symmetry type. We also prove the local version of the semicircle law on the optimal scale.","lang":"eng"}],"volume":56,"related_material":{"record":[{"status":"public","id":"149","relation":"dissertation_contains"}]},"issue":"10","ec_funded":1,"language":[{"iso":"eng"}],"publication_status":"published","status":"public","type":"journal_article","_id":"1677","department":[{"_id":"LaEr"}],"date_updated":"2023-09-07T12:38:08Z","quality_controlled":"1","publisher":"American Institute of Physics","oa":1,"doi":"10.1063/1.4932606","date_published":"2015-10-09T00:00:00Z","date_created":"2018-12-11T11:53:25Z","day":"09","publication":"Journal of Mathematical Physics","year":"2015","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_number":"103301","title":"The local semicircle law for random matrices with a fourfold symmetry","author":[{"full_name":"Alt, Johannes","last_name":"Alt","first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"5472","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Alt J. 2015. The local semicircle law for random matrices with a fourfold symmetry. Journal of Mathematical Physics. 56(10), 103301.","chicago":"Alt, Johannes. “The Local Semicircle Law for Random Matrices with a Fourfold Symmetry.” Journal of Mathematical Physics. American Institute of Physics, 2015. https://doi.org/10.1063/1.4932606.","apa":"Alt, J. (2015). The local semicircle law for random matrices with a fourfold symmetry. Journal of Mathematical Physics. American Institute of Physics. https://doi.org/10.1063/1.4932606","ama":"Alt J. The local semicircle law for random matrices with a fourfold symmetry. Journal of Mathematical Physics. 2015;56(10). doi:10.1063/1.4932606","ieee":"J. Alt, “The local semicircle law for random matrices with a fourfold symmetry,” Journal of Mathematical Physics, vol. 56, no. 10. American Institute of Physics, 2015.","short":"J. Alt, Journal of Mathematical Physics 56 (2015).","mla":"Alt, Johannes. “The Local Semicircle Law for Random Matrices with a Fourfold Symmetry.” Journal of Mathematical Physics, vol. 56, no. 10, 103301, American Institute of Physics, 2015, doi:10.1063/1.4932606."}},{"language":[{"iso":"eng"}],"publication_status":"published","issue":"3-4","volume":17,"ec_funded":1,"oa_version":"Preprint","abstract":[{"text":"We consider cross products of finite graphs with a class of trees that have arbitrarily but finitely long line segments, such as the Fibonacci tree. Such cross products are called tree-strips. We prove that for small disorder random Schrödinger operators on such tree-strips have purely absolutely continuous spectrum in a certain set.","lang":"eng"}],"month":"12","intvolume":" 17","scopus_import":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1304.3862"}],"date_updated":"2021-01-12T06:54:07Z","department":[{"_id":"LaEr"}],"_id":"1926","status":"public","type":"journal_article","article_type":"original","day":"17","publication":"Mathematical Physics, Analysis and Geometry","year":"2014","doi":"10.1007/s11040-014-9163-4","date_published":"2014-12-17T00:00:00Z","date_created":"2018-12-11T11:54:45Z","page":"409 - 440","publisher":"Springer","quality_controlled":"1","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Sadel C. 2014. Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips. Mathematical Physics, Analysis and Geometry. 17(3–4), 409–440.","chicago":"Sadel, Christian. “Absolutely Continuous Spectrum for Random Schrödinger Operators on the Fibonacci and Similar Tree-Strips.” Mathematical Physics, Analysis and Geometry. Springer, 2014. https://doi.org/10.1007/s11040-014-9163-4.","apa":"Sadel, C. (2014). Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips. Mathematical Physics, Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-014-9163-4","ama":"Sadel C. Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips. Mathematical Physics, Analysis and Geometry. 2014;17(3-4):409-440. doi:10.1007/s11040-014-9163-4","short":"C. Sadel, Mathematical Physics, Analysis and Geometry 17 (2014) 409–440.","ieee":"C. Sadel, “Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips,” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4. Springer, pp. 409–440, 2014.","mla":"Sadel, Christian. “Absolutely Continuous Spectrum for Random Schrödinger Operators on the Fibonacci and Similar Tree-Strips.” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4, Springer, 2014, pp. 409–40, doi:10.1007/s11040-014-9163-4."},"title":"Absolutely continuous spectrum for random Schrödinger operators on the Fibonacci and similar Tree-strips","publist_id":"5168","author":[{"id":"4760E9F8-F248-11E8-B48F-1D18A9856A87","first_name":"Christian","full_name":"Sadel, Christian","orcid":"0000-0001-8255-3968","last_name":"Sadel"}],"article_processing_charge":"No","external_id":{"arxiv":["1304.3862"]},"project":[{"_id":"26450934-B435-11E9-9278-68D0E5697425","name":"NSERC Postdoctoral fellowship"},{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}]},{"project":[{"_id":"25BDE9A4-B435-11E9-9278-68D0E5697425","name":"Glutamaterge synaptische Übertragung und Plastizität in hippocampalen Mikroschaltkreisen","grant_number":"SFB-TR3-TP10B"}],"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Bourgade P, Erdös L, Yau H. 2014. Edge universality of beta ensembles. Communications in Mathematical Physics. 332(1), 261–353.","chicago":"Bourgade, Paul, László Erdös, and Horngtzer Yau. “Edge Universality of Beta Ensembles.” Communications in Mathematical Physics. Springer, 2014. https://doi.org/10.1007/s00220-014-2120-z.","ama":"Bourgade P, Erdös L, Yau H. Edge universality of beta ensembles. Communications in Mathematical Physics. 2014;332(1):261-353. doi:10.1007/s00220-014-2120-z","apa":"Bourgade, P., Erdös, L., & Yau, H. (2014). Edge universality of beta ensembles. Communications in Mathematical Physics. Springer. https://doi.org/10.1007/s00220-014-2120-z","short":"P. Bourgade, L. Erdös, H. Yau, Communications in Mathematical Physics 332 (2014) 261–353.","ieee":"P. Bourgade, L. Erdös, and H. Yau, “Edge universality of beta ensembles,” Communications in Mathematical Physics, vol. 332, no. 1. Springer, pp. 261–353, 2014.","mla":"Bourgade, Paul, et al. “Edge Universality of Beta Ensembles.” Communications in Mathematical Physics, vol. 332, no. 1, Springer, 2014, pp. 261–353, doi:10.1007/s00220-014-2120-z."},"title":"Edge universality of beta ensembles","publist_id":"5158","author":[{"first_name":"Paul","last_name":"Bourgade","full_name":"Bourgade, Paul"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"full_name":"Yau, Horngtzer","last_name":"Yau","first_name":"Horngtzer"}],"oa":1,"quality_controlled":"1","publisher":"Springer","publication":"Communications in Mathematical Physics","day":"01","year":"2014","date_created":"2018-12-11T11:54:48Z","date_published":"2014-11-01T00:00:00Z","doi":"10.1007/s00220-014-2120-z","page":"261 - 353","_id":"1937","status":"public","type":"journal_article","date_updated":"2021-01-12T06:54:12Z","department":[{"_id":"LaEr"}],"oa_version":"Submitted Version","abstract":[{"lang":"eng","text":"We prove the edge universality of the beta ensembles for any β ≥ 1, provided that the limiting spectrum is supported on a single interval, and the external potential is C4 and regular. We also prove that the edge universality holds for generalized Wigner matrices for all symmetry classes. Moreover, our results allow us to extend bulk universality for beta ensembles from analytic potentials to potentials in class C4."}],"intvolume":" 332","month":"11","main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1306.5728"}],"scopus_import":1,"language":[{"iso":"eng"}],"publication_status":"published","volume":332,"issue":"1"},{"ec_funded":1,"issue":"3-4","volume":17,"publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1407.1552"}],"scopus_import":1,"intvolume":" 17","month":"12","abstract":[{"text":"We prove that the empirical density of states of quantum spin glasses on arbitrary graphs converges to a normal distribution as long as the maximal degree is negligible compared with the total number of edges. This extends the recent results of Keating et al. (2014) that were proved for graphs with bounded chromatic number and with symmetric coupling distribution. Furthermore, we generalise the result to arbitrary hypergraphs. We test the optimality of our condition on the maximal degree for p-uniform hypergraphs that correspond to p-spin glass Hamiltonians acting on n distinguishable spin- 1/2 particles. At the critical threshold p = n1/2 we find a sharp classical-quantum phase transition between the normal distribution and the Wigner semicircle law. The former is characteristic to classical systems with commuting variables, while the latter is a signature of noncommutative random matrix theory.","lang":"eng"}],"oa_version":"Submitted Version","department":[{"_id":"LaEr"}],"date_updated":"2021-01-12T06:54:45Z","type":"journal_article","status":"public","_id":"2019","page":"441 - 464","date_created":"2018-12-11T11:55:15Z","date_published":"2014-12-17T00:00:00Z","doi":"10.1007/s11040-014-9164-3","year":"2014","publication":"Mathematical Physics, Analysis and Geometry","day":"17","oa":1,"quality_controlled":"1","publisher":"Springer","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","first_name":"Dominik J"}],"publist_id":"5053","title":"Phase transition in the density of states of quantum spin glasses","citation":{"mla":"Erdös, László, and Dominik J. Schröder. “Phase Transition in the Density of States of Quantum Spin Glasses.” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4, Springer, 2014, pp. 441–64, doi:10.1007/s11040-014-9164-3.","short":"L. Erdös, D.J. Schröder, Mathematical Physics, Analysis and Geometry 17 (2014) 441–464.","ieee":"L. Erdös and D. J. Schröder, “Phase transition in the density of states of quantum spin glasses,” Mathematical Physics, Analysis and Geometry, vol. 17, no. 3–4. Springer, pp. 441–464, 2014.","ama":"Erdös L, Schröder DJ. Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry. 2014;17(3-4):441-464. doi:10.1007/s11040-014-9164-3","apa":"Erdös, L., & Schröder, D. J. (2014). Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry. Springer. https://doi.org/10.1007/s11040-014-9164-3","chicago":"Erdös, László, and Dominik J Schröder. “Phase Transition in the Density of States of Quantum Spin Glasses.” Mathematical Physics, Analysis and Geometry. Springer, 2014. https://doi.org/10.1007/s11040-014-9164-3.","ista":"Erdös L, Schröder DJ. 2014. Phase transition in the density of states of quantum spin glasses. Mathematical Physics, Analysis and Geometry. 17(3–4), 441–464."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}]},{"publication_status":"published","file":[{"file_size":327322,"date_updated":"2020-07-14T12:45:31Z","creator":"system","file_name":"IST-2016-426-v1+1_3121-17518-1-PB.pdf","date_created":"2018-12-12T10:09:06Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_id":"4729","checksum":"bd8a041c76d62fe820bf73ff13ce7d1b"}],"language":[{"iso":"eng"}],"volume":19,"abstract":[{"text":"We extend the proof of the local semicircle law for generalized Wigner matrices given in MR3068390 to the case when the matrix of variances has an eigenvalue -1. In particular, this result provides a short proof of the optimal local Marchenko-Pastur law at the hard edge (i.e. around zero) for sample covariance matrices X*X, where the variances of the entries of X may vary.","lang":"eng"}],"oa_version":"Published Version","scopus_import":1,"month":"06","intvolume":" 19","date_updated":"2021-01-12T06:55:48Z","ddc":["570"],"department":[{"_id":"LaEr"}],"file_date_updated":"2020-07-14T12:45:31Z","_id":"2179","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","pubrep_id":"426","has_accepted_license":"1","year":"2014","day":"09","publication":"Electronic Communications in Probability","doi":"10.1214/ECP.v19-3121","date_published":"2014-06-09T00:00:00Z","date_created":"2018-12-11T11:56:10Z","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"citation":{"chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Local Semicircle Law with Imprimitive Variance Matrix.” Electronic Communications in Probability. Institute of Mathematical Statistics, 2014. https://doi.org/10.1214/ECP.v19-3121.","ista":"Ajanki OH, Erdös L, Krüger TH. 2014. Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability. 19.","mla":"Ajanki, Oskari H., et al. “Local Semicircle Law with Imprimitive Variance Matrix.” Electronic Communications in Probability, vol. 19, Institute of Mathematical Statistics, 2014, doi:10.1214/ECP.v19-3121.","ama":"Ajanki OH, Erdös L, Krüger TH. Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability. 2014;19. doi:10.1214/ECP.v19-3121","apa":"Ajanki, O. H., Erdös, L., & Krüger, T. H. (2014). Local semicircle law with imprimitive variance matrix. Electronic Communications in Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/ECP.v19-3121","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Local semicircle law with imprimitive variance matrix,” Electronic Communications in Probability, vol. 19. Institute of Mathematical Statistics, 2014.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Electronic Communications in Probability 19 (2014)."},"user_id":"4435EBFC-F248-11E8-B48F-1D18A9856A87","author":[{"last_name":"Ajanki","full_name":"Ajanki, Oskari H","first_name":"Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"}],"publist_id":"4803","title":"Local semicircle law with imprimitive variance matrix"},{"article_number":"33","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"citation":{"ieee":"A. Bloemendal, L. Erdös, A. Knowles, H. Yau, and J. Yin, “Isotropic local laws for sample covariance and generalized Wigner matrices,” Electronic Journal of Probability, vol. 19. Institute of Mathematical Statistics, 2014.","short":"A. Bloemendal, L. Erdös, A. Knowles, H. Yau, J. Yin, Electronic Journal of Probability 19 (2014).","apa":"Bloemendal, A., Erdös, L., Knowles, A., Yau, H., & Yin, J. (2014). Isotropic local laws for sample covariance and generalized Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/EJP.v19-3054","ama":"Bloemendal A, Erdös L, Knowles A, Yau H, Yin J. Isotropic local laws for sample covariance and generalized Wigner matrices. Electronic Journal of Probability. 2014;19. doi:10.1214/EJP.v19-3054","mla":"Bloemendal, Alex, et al. “Isotropic Local Laws for Sample Covariance and Generalized Wigner Matrices.” Electronic Journal of Probability, vol. 19, 33, Institute of Mathematical Statistics, 2014, doi:10.1214/EJP.v19-3054.","ista":"Bloemendal A, Erdös L, Knowles A, Yau H, Yin J. 2014. Isotropic local laws for sample covariance and generalized Wigner matrices. Electronic Journal of Probability. 19, 33.","chicago":"Bloemendal, Alex, László Erdös, Antti Knowles, Horng Yau, and Jun Yin. “Isotropic Local Laws for Sample Covariance and Generalized Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2014. https://doi.org/10.1214/EJP.v19-3054."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publist_id":"4739","author":[{"first_name":"Alex","last_name":"Bloemendal","full_name":"Bloemendal, Alex"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"last_name":"Knowles","full_name":"Knowles, Antti","first_name":"Antti"},{"first_name":"Horng","full_name":"Yau, Horng","last_name":"Yau"},{"last_name":"Yin","full_name":"Yin, Jun","first_name":"Jun"}],"title":"Isotropic local laws for sample covariance and generalized Wigner matrices","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","year":"2014","has_accepted_license":"1","publication":"Electronic Journal of Probability","day":"15","date_created":"2018-12-11T11:56:25Z","doi":"10.1214/EJP.v19-3054","date_published":"2014-03-15T00:00:00Z","_id":"2225","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","pubrep_id":"427","status":"public","date_updated":"2021-01-12T06:56:07Z","ddc":["510"],"department":[{"_id":"LaEr"}],"file_date_updated":"2020-07-14T12:45:34Z","abstract":[{"text":"We consider sample covariance matrices of the form X∗X, where X is an M×N matrix with independent random entries. We prove the isotropic local Marchenko-Pastur law, i.e. we prove that the resolvent (X∗X−z)−1 converges to a multiple of the identity in the sense of quadratic forms. More precisely, we establish sharp high-probability bounds on the quantity ⟨v,(X∗X−z)−1w⟩−⟨v,w⟩m(z), where m is the Stieltjes transform of the Marchenko-Pastur law and v,w∈CN. We require the logarithms of the dimensions M and N to be comparable. Our result holds down to scales Iz≥N−1+ε and throughout the entire spectrum away from 0. We also prove analogous results for generalized Wigner matrices.\r\n","lang":"eng"}],"oa_version":"Published Version","intvolume":" 19","month":"03","publication_status":"published","publication_identifier":{"issn":["10836489"]},"language":[{"iso":"eng"}],"file":[{"file_id":"5055","checksum":"7eb297ff367a2ee73b21b6dd1e1948e4","content_type":"application/pdf","access_level":"open_access","relation":"main_file","date_created":"2018-12-12T10:14:06Z","file_name":"IST-2016-427-v1+1_3054-16624-4-PB.pdf","date_updated":"2020-07-14T12:45:34Z","file_size":810150,"creator":"system"}],"ec_funded":1,"volume":19},{"month":"04","intvolume":" 163","publisher":"Duke University Press","quality_controlled":"1","scopus_import":1,"main_file_link":[{"open_access":"1","url":"http://arxiv.org/abs/1104.2272"}],"oa":1,"oa_version":"Preprint","abstract":[{"lang":"eng","text":"We prove the universality of the β-ensembles with convex analytic potentials and for any β >\r\n0, i.e. we show that the spacing distributions of log-gases at any inverse temperature β coincide with those of the Gaussian β-ensembles."}],"date_published":"2014-04-01T00:00:00Z","volume":163,"doi":"10.1215/00127094-2649752","issue":"6","date_created":"2018-12-11T11:59:08Z","page":"1127 - 1190","day":"01","publication":"Duke Mathematical Journal","language":[{"iso":"eng"}],"publication_status":"published","year":"2014","status":"public","type":"journal_article","_id":"2699","department":[{"_id":"LaEr"}],"title":"Universality of general β-ensembles","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"first_name":"Paul","full_name":"Bourgade, Paul","last_name":"Bourgade"},{"last_name":"Yau","full_name":"Yau, Horng","first_name":"Horng"}],"publist_id":"4197","user_id":"3FFCCD3A-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T06:59:07Z","citation":{"mla":"Erdös, László, et al. “Universality of General β-Ensembles.” Duke Mathematical Journal, vol. 163, no. 6, Duke University Press, 2014, pp. 1127–90, doi:10.1215/00127094-2649752.","ieee":"L. Erdös, P. Bourgade, and H. Yau, “Universality of general β-ensembles,” Duke Mathematical Journal, vol. 163, no. 6. Duke University Press, pp. 1127–1190, 2014.","short":"L. Erdös, P. Bourgade, H. Yau, Duke Mathematical Journal 163 (2014) 1127–1190.","apa":"Erdös, L., Bourgade, P., & Yau, H. (2014). Universality of general β-ensembles. Duke Mathematical Journal. Duke University Press. https://doi.org/10.1215/00127094-2649752","ama":"Erdös L, Bourgade P, Yau H. Universality of general β-ensembles. Duke Mathematical Journal. 2014;163(6):1127-1190. doi:10.1215/00127094-2649752","chicago":"Erdös, László, Paul Bourgade, and Horng Yau. “Universality of General β-Ensembles.” Duke Mathematical Journal. Duke University Press, 2014. https://doi.org/10.1215/00127094-2649752.","ista":"Erdös L, Bourgade P, Yau H. 2014. Universality of general β-ensembles. Duke Mathematical Journal. 163(6), 1127–1190."}}]