[{"abstract":[{"lang":"eng","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."}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2012.15238"}],"intvolume":" 63","month":"01","publication_status":"published","publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"language":[{"iso":"eng"}],"ec_funded":1,"volume":63,"issue":"1","_id":"10600","type":"journal_article","article_type":"original","keyword":["mathematical physics","statistical and nonlinear physics"],"status":"public","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.","oa":1,"publisher":"AIP Publishing","quality_controlled":"1","year":"2022","isi":1,"publication":"Journal of Mathematical Physics","day":"03","date_created":"2022-01-03T12:19:48Z","date_published":"2022-01-03T00:00:00Z","doi":"10.1063/5.0051632","article_number":"011901","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"citation":{"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","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.","short":"S.J. Henheik, S. Teufel, Journal of Mathematical Physics 63 (2022).","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.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000739446000009"],"arxiv":["2012.15238"]},"author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik"},{"first_name":"Stefan","full_name":"Teufel, Stefan","last_name":"Teufel"}],"title":"Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap"},{"issue":"1","volume":112,"ec_funded":1,"file":[{"file_name":"2022_LettersMathPhys_Henheik.pdf","date_created":"2022-01-19T09:41:14Z","file_size":357547,"date_updated":"2022-01-19T09:41:14Z","creator":"cchlebak","success":1,"file_id":"10647","checksum":"7e8e69b76e892c305071a4736131fe18","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"publication_status":"published","month":"01","intvolume":" 112","oa_version":"Published Version","abstract":[{"lang":"eng","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."}],"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","doi":"10.1007/s11005-021-01494-y","date_published":"2022-01-18T00:00:00Z","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.","title":"Local stability of ground states in locally gapped and weakly interacting quantum spin systems","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik"},{"full_name":"Teufel, Stefan","last_name":"Teufel","first_name":"Stefan"},{"full_name":"Wessel, Tom","last_name":"Wessel","first_name":"Tom"}],"external_id":{"isi":["000744930400001"],"arxiv":["2106.13780"]},"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.","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","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","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).","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"},{"oa_version":"Published Version","abstract":[{"lang":"eng","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"}],"month":"01","intvolume":" 10","file":[{"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","success":1,"checksum":"87592a755adcef22ea590a99dc728dd3","file_id":"10646","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"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"],"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":"2023-08-02T13:53:11Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-19T09:27:43Z","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","doi":"10.1017/fms.2021.80","date_published":"2022-01-18T00:00:00Z","date_created":"2022-01-18T16:18:51Z","article_number":"e4","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma, vol. 10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022.","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","apa":"Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.80","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2021.80","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” Forum of Mathematics, Sigma. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2021.80.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4."},"title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha"},{"last_name":"Teufel","full_name":"Teufel, Stefan","first_name":"Stefan"}],"article_processing_charge":"Yes","external_id":{"arxiv":["2012.15239"],"isi":["000743615000001"]}},{"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"article_number":"3","external_id":{"isi":["000741387600001"],"arxiv":["2106.02015"]},"article_processing_charge":"Yes (via OA deal)","author":[{"full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"}],"title":"The BCS critical temperature at high density","citation":{"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.","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","ama":"Henheik SJ. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 2022;25(1). doi:10.1007/s11040-021-09415-0","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","oa":1,"publisher":"Springer Nature","quality_controlled":"1","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.","date_created":"2022-01-13T15:40:53Z","doi":"10.1007/s11040-021-09415-0","date_published":"2022-01-11T00:00:00Z","year":"2022","isi":1,"has_accepted_license":"1","publication":"Mathematical Physics, Analysis and Geometry","day":"11","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","keyword":["geometry and topology","mathematical physics"],"status":"public","_id":"10623","file_date_updated":"2022-01-14T07:27:45Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_updated":"2023-08-02T13:51:52Z","ddc":["514"],"scopus_import":"1","intvolume":" 25","month":"01","abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","ec_funded":1,"issue":"1","volume":25,"publication_status":"published","publication_identifier":{"eissn":["1572-9656"],"issn":["1385-0172"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2022_MathPhyAnalGeo_Henheik.pdf","date_created":"2022-01-14T07:27:45Z","creator":"cchlebak","file_size":505804,"date_updated":"2022-01-14T07:27:45Z","success":1,"file_id":"10624","checksum":"d44f8123a52592a75b2c3b8ee2cd2435","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}]},{"oa":1,"publisher":"Elsevier","quality_controlled":"1","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.","date_created":"2022-02-06T23:01:30Z","doi":"10.1016/j.jfa.2022.109394","date_published":"2022-04-15T00:00:00Z","publication":"Journal of Functional Analysis","day":"15","year":"2022","has_accepted_license":"1","isi":1,"article_number":"109394","title":"Thermalisation for Wigner matrices","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000781239100004"],"arxiv":["2102.09975"]},"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"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","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” Journal of Functional Analysis, vol. 282, no. 8. Elsevier, 2022.","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","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","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.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394."},"intvolume":" 282","month":"04","scopus_import":"1","oa_version":"Published Version","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"}],"issue":"8","volume":282,"language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"checksum":"b75fdad606ab507dc61109e0907d86c0","file_id":"11690","creator":"dernst","file_size":652573,"date_updated":"2022-07-29T07:22:08Z","file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","date_created":"2022-07-29T07:22:08Z"}],"publication_status":"published","publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"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","_id":"10732","department":[{"_id":"LaEr"}],"file_date_updated":"2022-07-29T07:22:08Z","ddc":["500"],"date_updated":"2023-08-02T14:12:35Z"},{"abstract":[{"lang":"eng","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."}],"oa_version":"Preprint","main_file_link":[{"url":" https://doi.org/10.48550/arXiv.2103.03906","open_access":"1"}],"scopus_import":"1","intvolume":" 11","month":"10","publication_status":"published","publication_identifier":{"eissn":["2010-3271"],"issn":["2010-3263"]},"language":[{"iso":"eng"}],"volume":11,"issue":"4","_id":"11135","type":"journal_article","article_type":"original","keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"status":"public","date_updated":"2023-08-03T06:32:22Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"oa":1,"quality_controlled":"1","publisher":"World Scientific","year":"2022","isi":1,"publication":"Random Matrices: Theory and Applications","day":"01","date_created":"2022-04-08T07:11:12Z","doi":"10.1142/s2010326322500368","date_published":"2022-10-01T00:00:00Z","article_number":"2250036","citation":{"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","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.","short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","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.","ista":"Reker J. 2022. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 11(4), 2250036.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000848873800001"],"arxiv":["2103.03906"]},"author":[{"first_name":"Jana","id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","last_name":"Reker","full_name":"Reker, Jana"}],"title":"On the operator norm of a Hermitian random matrix with correlated entries"},{"language":[{"iso":"eng"}],"file":[{"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","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","file_id":"11726","success":1}],"publication_status":"published","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"ec_funded":1,"volume":393,"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."}],"intvolume":" 393","month":"07","scopus_import":"1","ddc":["510"],"date_updated":"2023-08-03T06:34:24Z","file_date_updated":"2022-08-05T06:01:13Z","department":[{"_id":"LaEr"}],"_id":"11332","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","publication":"Communications in Mathematical Physics","day":"01","year":"2022","has_accepted_license":"1","isi":1,"date_created":"2022-04-24T22:01:44Z","doi":"10.1007/s00220-022-04377-y","date_published":"2022-07-01T00:00:00Z","page":"839-907","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.","oa":1,"quality_controlled":"1","publisher":"Springer Nature","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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.","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907.","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","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","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."},"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":[{"last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin"},{"full_name":"Xu, Yuanyuan","last_name":"Xu","first_name":"Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3"}],"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}]},{"status":"public","article_type":"original","type":"journal_article","_id":"11418","department":[{"_id":"LaEr"}],"date_updated":"2023-08-03T07:16:53Z","intvolume":" 50","month":"05","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng","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)."}],"volume":50,"issue":"3","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"title":"Normal fluctuation in quantum ergodicity for Wigner matrices","article_processing_charge":"No","external_id":{"isi":["000793963400005"],"arxiv":["2103.06730"]},"author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-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"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annals of Probability 50 (2022) 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.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012."},"oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","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.","date_created":"2022-05-29T22:01:53Z","date_published":"2022-05-01T00:00:00Z","doi":"10.1214/21-AOP1552","page":"984-1012","publication":"Annals of Probability","day":"01","year":"2022","isi":1},{"file":[{"creator":"dernst","date_updated":"2023-01-20T11:58:59Z","file_size":5436804,"date_created":"2023-01-20T11:58:59Z","file_name":"2022_JourMathPhysics_Henheik.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"12327","checksum":"5150287295e0ce4f12462c990744d65d","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-2488"]},"publication_status":"published","volume":63,"issue":"12","ec_funded":1,"oa_version":"Published Version","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."}],"month":"12","intvolume":" 63","scopus_import":"1","ddc":["510"],"date_updated":"2023-08-03T14:12:01Z","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-20T11:58:59Z","_id":"12110","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)"},"day":"01","publication":"Journal of Mathematical Physics","isi":1,"has_accepted_license":"1","year":"2022","doi":"10.1063/5.0104675","date_published":"2022-12-01T00:00:00Z","date_created":"2023-01-08T23:00:53Z","acknowledgement":"J.H. gratefully acknowledges the partial financial support by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n","publisher":"AIP Publishing","quality_controlled":"1","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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","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.","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."},"title":"Interior-boundary conditions for the Dirac equation at point sources in three dimensions","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha"},{"first_name":"Roderich","full_name":"Tumulka, Roderich","last_name":"Tumulka"}],"external_id":{"isi":["000900748900002"]},"article_processing_charge":"No","article_number":"122302","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}]},{"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.","quality_controlled":"1","publisher":"Cambridge University Press","oa":1,"has_accepted_license":"1","isi":1,"year":"2022","day":"27","publication":"Forum of Mathematics, Sigma","doi":"10.1017/fms.2022.86","date_published":"2022-10-27T00:00:00Z","date_created":"2023-01-12T12:07:30Z","article_number":"e96","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"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","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (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","author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"external_id":{"isi":["000873719200001"]},"article_processing_charge":"No","title":"Rank-uniform local law for Wigner matrices","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","scopus_import":"1","month":"10","intvolume":" 10","publication_identifier":{"issn":["2050-5094"]},"publication_status":"published","file":[{"creator":"dernst","file_size":817089,"date_updated":"2023-01-24T10:02:40Z","file_name":"2022_ForumMath_Cipolloni.pdf","date_created":"2023-01-24T10:02:40Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"12356","checksum":"94a049aeb1eea5497aa097712a73c400"}],"language":[{"iso":"eng"}],"volume":10,"ec_funded":1,"_id":"12148","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":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"date_updated":"2023-08-04T09:00:35Z","ddc":["510"],"file_date_updated":"2023-01-24T10:02:40Z","department":[{"_id":"LaEr"}]},{"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.\" ","oa":1,"quality_controlled":"1","publisher":"AIP Publishing","publication":"Journal of Mathematical Physics","day":"01","year":"2022","has_accepted_license":"1","isi":1,"date_created":"2023-01-15T23:00:52Z","date_published":"2022-12-01T00:00:00Z","doi":"10.1063/5.0123441","article_number":"121101","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":{"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.","ista":"Henheik SJ, Wessel T. 2022. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 63(12), 121101.","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.","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","short":"S.J. Henheik, T. Wessel, Journal of Mathematical Physics 63 (2022).","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."},"title":"On adiabatic theory for extended fermionic lattice systems","article_processing_charge":"No","external_id":{"isi":["000905776200001"],"arxiv":["2208.12220"]},"author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha","last_name":"Henheik","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X"},{"full_name":"Wessel, Tom","last_name":"Wessel","first_name":"Tom"}],"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"}],"intvolume":" 63","month":"12","scopus_import":"1","language":[{"iso":"eng"}],"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"}],"publication_status":"published","publication_identifier":{"issn":["0022-2488"]},"ec_funded":1,"volume":63,"issue":"12","_id":"12184","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":"2023-08-04T09:14:57Z","file_date_updated":"2023-01-27T07:10:52Z","department":[{"_id":"LaEr"}]},{"date_updated":"2023-08-04T09:24:17Z","department":[{"_id":"LaEr"}],"_id":"12214","type":"journal_article","article_type":"original","status":"public","keyword":["General Mathematics"],"publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"4","volume":106,"ec_funded":1,"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","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2102.02037","open_access":"1"}],"month":"09","intvolume":" 106","citation":{"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","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.","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society 106 (2022) 3865–3894.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"first_name":"György Pál","full_name":"Gehér, György Pál","last_name":"Gehér"},{"first_name":"Tamás","last_name":"Titkos","full_name":"Titkos, Tamás"},{"first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511"}],"article_processing_charge":"No","external_id":{"isi":["000854878500001"],"arxiv":["2102.02037"]},"title":"The isometry group of Wasserstein spaces: The Hilbertian case","project":[{"name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"isi":1,"year":"2022","day":"18","publication":"Journal of the London Mathematical Society","page":"3865-3894","date_published":"2022-09-18T00:00:00Z","doi":"10.1112/jlms.12676","date_created":"2023-01-16T09:46:13Z","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). ","publisher":"Wiley","quality_controlled":"1","oa":1},{"file":[{"date_updated":"2023-01-27T11:06:47Z","file_size":1333638,"creator":"dernst","date_created":"2023-01-27T11:06:47Z","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","file_id":"12424","checksum":"5582f059feeb2f63e2eb68197a34d7dc","success":1}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"publication_status":"published","issue":"11","volume":23,"oa_version":"Published Version","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"}],"month":"11","intvolume":" 23","scopus_import":"1","ddc":["510"],"date_updated":"2023-08-04T09:33:52Z","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-27T11:06:47Z","_id":"12232","status":"public","keyword":["Mathematical Physics","Nuclear and High Energy 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)"},"day":"01","publication":"Annales Henri Poincaré","has_accepted_license":"1","isi":1,"year":"2022","date_published":"2022-11-01T00:00:00Z","doi":"10.1007/s00023-022-01188-8","date_created":"2023-01-16T09:50:26Z","page":"3981-4002","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.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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.","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","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."},"title":"Density of small singular values of the shifted real Ginibre ensemble","author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-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"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"article_processing_charge":"No","external_id":{"isi":["000796323500001"]}},{"oa_version":"Published Version","abstract":[{"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)]. ","lang":"eng"}],"intvolume":" 63","month":"10","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"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","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"2db278ae5b07f345a7e3fec1f92b5c33","file_id":"12436"}],"publication_status":"published","publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"ec_funded":1,"volume":63,"issue":"10","_id":"12243","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"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":["510","530"],"date_updated":"2023-08-04T09:40:02Z","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-30T08:01:10Z","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.","oa":1,"quality_controlled":"1","publisher":"AIP Publishing","publication":"Journal of Mathematical Physics","day":"14","year":"2022","isi":1,"has_accepted_license":"1","date_created":"2023-01-16T09:52:58Z","doi":"10.1063/5.0104290","date_published":"2022-10-14T00:00:00Z","article_number":"103303","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":{"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","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","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022).","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.","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."},"title":"Directional extremal statistics for Ginibre eigenvalues","external_id":{"isi":["000869715800001"],"arxiv":["2206.04443"]},"article_processing_charge":"Yes (via OA deal)","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"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan","full_name":"Xu, Yuanyuan","last_name":"Xu"}]},{"year":"2022","has_accepted_license":"1","isi":1,"publication":"Electronic Journal of Probability","day":"12","page":"1-38","date_created":"2023-01-16T10:04:38Z","doi":"10.1214/22-ejp838","date_published":"2022-09-12T00:00:00Z","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.","oa":1,"quality_controlled":"1","publisher":"Institute of Mathematical Statistics","citation":{"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.","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.","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","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","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000910863700003"]},"article_processing_charge":"No","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"title":"Optimal multi-resolvent local laws for Wigner matrices","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"publication_status":"published","publication_identifier":{"eissn":["1083-6489"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"checksum":"bb647b48fbdb59361210e425c220cdcb","file_id":"12464","file_size":502149,"date_updated":"2023-01-30T11:59:21Z","creator":"dernst","file_name":"2022_ElecJournProbability_Cipolloni.pdf","date_created":"2023-01-30T11:59:21Z"}],"ec_funded":1,"volume":27,"abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 27","month":"09","date_updated":"2023-08-04T10:32:23Z","ddc":["510"],"file_date_updated":"2023-01-30T11:59:21Z","department":[{"_id":"LaEr"}],"_id":"12290","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","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"status":"public"},{"date_created":"2022-08-05T11:36:56Z","doi":"10.1007/s10955-022-02965-9","date_published":"2022-07-29T00:00:00Z","publication":"Journal of Statistical Physics","day":"29","year":"2022","isi":1,"has_accepted_license":"1","oa":1,"quality_controlled":"1","publisher":"Springer Nature","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)","title":"The BCS energy gap at high density","external_id":{"isi":["000833007200002"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"last_name":"Lauritsen","full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","ista":"Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5.","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.","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.","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","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"},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"article_number":"5","ec_funded":1,"volume":189,"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"b398c4dbf65f71d417981d6e366427e9","file_id":"11746","success":1,"date_updated":"2022-08-08T07:36:34Z","file_size":419563,"creator":"dernst","date_created":"2022-08-08T07:36:34Z","file_name":"2022_JourStatisticalPhysics_Henheik.pdf"}],"publication_status":"published","publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"intvolume":" 189","month":"07","scopus_import":"1","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."}],"file_date_updated":"2022-08-08T07:36:34Z","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"ddc":["530"],"date_updated":"2023-09-05T14:57:49Z","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"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","_id":"11732"},{"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":"10285","file_date_updated":"2021-11-15T10:10:17Z","department":[{"_id":"LaEr"}],"ddc":["519"],"date_updated":"2021-11-15T10:48:46Z","month":"09","intvolume":" 26","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."}],"volume":26,"ec_funded":1,"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"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1083-6489"]},"publication_status":"published","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"article_number":"124","title":"On eigenvector statistics in the spherical and truncated unitary ensembles","author":[{"orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","last_name":"Dubach","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume"}],"article_processing_charge":"No","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"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.","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.","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","ama":"Dubach G. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 2021;26. doi: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."},"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":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.","doi":"10.1214/21-EJP686","date_published":"2021-09-28T00:00:00Z","date_created":"2021-11-14T23:01:25Z","day":"28","publication":"Electronic Journal of Probability","has_accepted_license":"1","year":"2021"},{"title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","department":[{"_id":"LaEr"}],"author":[{"last_name":"Arguin","full_name":"Arguin, Louis-Pierre","first_name":"Louis-Pierre"},{"orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","last_name":"Dubach","first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"},{"full_name":"Hartung, Lisa","last_name":"Hartung","first_name":"Lisa"}],"external_id":{"arxiv":["2103.04817"]},"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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.","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","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. ."},"date_updated":"2023-05-03T10:22:59Z","status":"public","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"type":"preprint","article_number":"2103.04817","_id":"9230","date_published":"2021-03-08T00:00:00Z","doi":"10.48550/arXiv.2103.04817","date_created":"2021-03-09T11:08:15Z","ec_funded":1,"day":"08","language":[{"iso":"eng"}],"publication":"arXiv","year":"2021","publication_status":"submitted","month":"03","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.04817"}],"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.","abstract":[{"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.","lang":"eng"}]},{"day":"21","language":[{"iso":"eng"}],"publication":"arXiv","publication_status":"submitted","year":"2021","date_published":"2021-03-21T00:00:00Z","doi":"10.48550/arXiv.2103.11389","related_material":{"record":[{"relation":"other","status":"public","id":"9946"}]},"date_created":"2021-03-23T05:38:48Z","ec_funded":1,"oa_version":"Preprint","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."}],"month":"03","main_file_link":[{"url":"https://arxiv.org/abs/2103.11389","open_access":"1"}],"oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2023-05-03T10:26:45Z","citation":{"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","short":"G. Dubach, F. Mühlböck, ArXiv (n.d.).","ieee":"G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,” arXiv. .","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."},"department":[{"_id":"LaEr"},{"_id":"ToHe"}],"title":"Formal verification of Zagier's one-sentence proof","author":[{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume","full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach"},{"id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425","first_name":"Fabian","full_name":"Mühlböck, Fabian","orcid":"0000-0003-1548-0177","last_name":"Mühlböck"}],"external_id":{"arxiv":["2103.11389"]},"article_processing_charge":"No","article_number":"2103.11389","_id":"9281","status":"public","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"type":"preprint"},{"main_file_link":[{"url":"https://arxiv.org/abs/2002.11678","open_access":"1"}],"month":"01","intvolume":" 609","abstract":[{"lang":"eng","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."}],"oa_version":"Preprint","volume":609,"ec_funded":1,"publication_identifier":{"issn":["0024-3795"]},"publication_status":"published","language":[{"iso":"eng"}],"article_type":"original","type":"journal_article","status":"public","keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"_id":"8373","department":[{"_id":"LaEr"}],"date_updated":"2023-08-04T10:58:14Z","publisher":"Elsevier","quality_controlled":"1","oa":1,"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_published":"2021-01-15T00:00:00Z","doi":"10.1016/j.laa.2020.09.007","date_created":"2020-09-11T08:35:50Z","isi":1,"year":"2021","day":"15","publication":"Linear Algebra and its Applications","project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425"},{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"author":[{"last_name":"Pitrik","full_name":"Pitrik, József","first_name":"József"},{"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":["2002.11678"],"isi":["000581730500011"]},"title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","citation":{"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","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","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.","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8"},{"_id":"9036","article_type":"original","type":"journal_article","status":"public","keyword":["General Mathematics"],"date_updated":"2023-08-07T13:34:48Z","department":[{"_id":"LaEr"}],"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"}],"oa_version":"Preprint","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1910.10447"}],"month":"03","intvolume":" 380","publication_identifier":{"issn":["0001-8708"]},"publication_status":"published","language":[{"iso":"eng"}],"issue":"3","volume":380,"ec_funded":1,"article_number":"107595","project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"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.","ista":"Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 380(3), 107595.","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.","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","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","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)."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel"}],"external_id":{"isi":["000619676100035"],"arxiv":["1910.10447"]},"article_processing_charge":"No","title":"The metric property of the quantum Jensen-Shannon divergence","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.","quality_controlled":"1","publisher":"Elsevier","oa":1,"isi":1,"year":"2021","day":"26","publication":"Advances in Mathematics","doi":"10.1016/j.aim.2021.107595","date_published":"2021-03-26T00:00:00Z","date_created":"2021-01-22T17:55:17Z"},{"volume":26,"ec_funded":1,"file":[{"date_created":"2021-05-25T13:24:19Z","file_name":"2021_EJP_Cipolloni.pdf","creator":"kschuh","date_updated":"2021-05-25T13:24:19Z","file_size":865148,"checksum":"864ab003ad4cffea783f65aa8c2ba69f","file_id":"9423","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["10836489"]},"publication_status":"published","month":"03","intvolume":" 26","scopus_import":"1","oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"file_date_updated":"2021-05-25T13:24:19Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2023-08-08T13:39:19Z","status":"public","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":"9412","doi":"10.1214/21-EJP591","date_published":"2021-03-23T00:00:00Z","date_created":"2021-05-23T22:01:44Z","day":"23","publication":"Electronic Journal of Probability","isi":1,"has_accepted_license":"1","year":"2021","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"title":"Fluctuation around the circular law for random matrices with real entries","author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"arxiv":["2002.02438"],"isi":["000641855600001"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 26 (2021).","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","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.","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.","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."},"project":[{"_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"665385","name":"International IST Doctoral Program"}],"article_number":"24"},{"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":[{"file_name":"2021_ForumMath_Bao.pdf","date_created":"2021-06-15T14:40:45Z","file_size":483458,"date_updated":"2021-06-15T14:40:45Z","creator":"cziletti","success":1,"file_id":"9555","checksum":"47c986578de132200d41e6d391905519","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["20505094"]},"publication_status":"published","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","department":[{"_id":"LaEr"}],"file_date_updated":"2021-06-15T14:40:45Z","ddc":["510"],"date_updated":"2023-08-08T14:03:40Z","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","doi":"10.1017/fms.2021.38","date_published":"2021-05-27T00:00:00Z","date_created":"2021-06-13T22:01:33Z","day":"27","publication":"Forum of Mathematics, Sigma","has_accepted_license":"1","isi":1,"year":"2021","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_number":"e44","title":"Equipartition principle for Wigner matrices","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","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","external_id":{"isi":["000654960800001"],"arxiv":["2008.07061"]},"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.","ama":"Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 2021;9. doi: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","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."}},{"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"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.","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","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","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"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"},{"id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy","last_name":"Nemish","full_name":"Nemish, Yuriy","orcid":"0000-0002-7327-856X"}],"article_processing_charge":"Yes (in subscription journal)","external_id":{"isi":["000681531500001"],"arxiv":["1911.05112"]},"title":"Scattering in quantum dots via noncommutative rational functions","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,"has_accepted_license":"1","isi":1,"year":"2021","day":"01","publication":"Annales Henri Poincaré ","page":"4205–4269","date_published":"2021-12-01T00:00:00Z","doi":"10.1007/s00023-021-01085-6","date_created":"2021-08-15T22:01:29Z","_id":"9912","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":"2023-08-11T10:31:48Z","ddc":["510"],"department":[{"_id":"LaEr"}],"file_date_updated":"2022-05-12T12:50:27Z","abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"12","intvolume":" 22","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"publication_status":"published","file":[{"success":1,"checksum":"8d6bac0e2b0a28539608b0538a8e3b38","file_id":"11365","relation":"main_file","access_level":"open_access","content_type":"application/pdf","file_name":"2021_AnnHenriPoincare_Erdoes.pdf","date_created":"2022-05-12T12:50:27Z","creator":"dernst","file_size":1162454,"date_updated":"2022-05-12T12:50:27Z"}],"language":[{"iso":"eng"}],"volume":22,"ec_funded":1},{"file_date_updated":"2022-02-02T10:19:55Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2023-08-14T10:29:49Z","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":"10221","issue":"2","volume":388,"file":[{"success":1,"checksum":"a2c7b6f5d23b5453cd70d1261272283b","file_id":"10715","content_type":"application/pdf","relation":"main_file","access_level":"open_access","file_name":"2021_CommunMathPhys_Cipolloni.pdf","date_created":"2022-02-02T10:19:55Z","file_size":841426,"date_updated":"2022-02-02T10:19:55Z","creator":"cchlebak"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"publication_status":"published","month":"10","intvolume":" 388","scopus_import":"1","oa_version":"Published Version","abstract":[{"lang":"eng","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)."}],"title":"Eigenstate thermalization hypothesis for Wigner matrices","author":[{"first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","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","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"external_id":{"arxiv":["2012.13215"],"isi":["000712232700001"]},"article_processing_charge":"Yes (via OA deal)","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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","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","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.","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."},"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"doi":"10.1007/s00220-021-04239-z","date_published":"2021-10-29T00:00:00Z","date_created":"2021-11-07T23:01:25Z","page":"1005–1048","day":"29","publication":"Communications in Mathematical Physics","isi":1,"has_accepted_license":"1","year":"2021","publisher":"Springer Nature","quality_controlled":"1","oa":1,"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria)."},{"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.","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","project":[{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","title":"Fluctuations in the spectrum of random matrices","citation":{"mla":"Cipolloni, Giorgio. Fluctuations in the Spectrum of Random Matrices. Institute of Science and Technology Austria, 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","ama":"Cipolloni G. Fluctuations in the spectrum of random matrices. 2021. doi: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.","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.","ista":"Cipolloni G. 2021. Fluctuations in the spectrum of random matrices. Institute of Science and Technology Austria."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","alternative_title":["ISTA Thesis"],"month":"01","abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","ec_funded":1,"publication_identifier":{"issn":["2663-337X"]},"publication_status":"published","degree_awarded":"PhD","file":[{"date_created":"2021-01-25T14:19:03Z","file_name":"thesis.pdf","creator":"gcipollo","date_updated":"2021-01-25T14:19:03Z","file_size":4127796,"checksum":"5a93658a5f19478372523ee232887e2b","file_id":"9043","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"},{"file_id":"9044","checksum":"e8270eddfe6a988e92a53c88d1d19b8c","access_level":"closed","relation":"source_file","content_type":"application/zip","date_created":"2021-01-25T14:19:10Z","file_name":"Thesis_files.zip","creator":"gcipollo","date_updated":"2021-01-25T14:19:10Z","file_size":12775206}],"language":[{"iso":"eng"}],"type":"dissertation","status":"public","_id":"9022","file_date_updated":"2021-01-25T14:19:10Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"supervisor":[{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2023-09-07T13:29:32Z","ddc":["510"]},{"date_updated":"2024-02-19T08:30:00Z","department":[{"_id":"LaEr"}],"_id":"15013","article_type":"original","type":"journal_article","status":"public","publication_status":"published","publication_identifier":{"issn":["2690-0998"],"eissn":["2690-1005"]},"language":[{"iso":"eng"}],"ec_funded":1,"issue":"2","volume":2,"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","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1907.13631","open_access":"1"}],"scopus_import":"1","intvolume":" 2","month":"05","citation":{"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","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","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.","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.","ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","external_id":{"arxiv":["1907.13631"]},"author":[{"first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","full_name":"Alt, Johannes"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger"}],"title":"Spectral radius of random matrices with independent entries","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"year":"2021","publication":"Probability and Mathematical Physics","day":"21","page":"221-280","date_created":"2024-02-18T23:01:03Z","doi":"10.2140/pmp.2021.2.221","date_published":"2021-05-21T00:00:00Z","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.","oa":1,"publisher":"Mathematical Sciences Publishers","quality_controlled":"1"},{"file_date_updated":"2020-10-05T14:53:40Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2024-03-07T15:07:53Z","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":"8601","ec_funded":1,"language":[{"iso":"eng"}],"file":[{"file_size":497032,"date_updated":"2020-10-05T14:53:40Z","creator":"dernst","file_name":"2020_ProbTheory_Cipolloni.pdf","date_created":"2020-10-05T14:53:40Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"8612","checksum":"611ae28d6055e1e298d53a57beb05ef4"}],"publication_status":"published","publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"month":"02","scopus_import":"1","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."}],"title":"Edge universality for non-Hermitian random matrices","external_id":{"arxiv":["1908.00969"],"isi":["000572724600002"]},"article_processing_charge":"Yes (via OA deal)","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.","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.","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","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.","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."},"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","name":"International IST Doctoral Program","grant_number":"665385"}],"date_created":"2020-10-04T22:01:37Z","doi":"10.1007/s00440-020-01003-7","date_published":"2021-02-01T00:00:00Z","publication":"Probability Theory and Related Fields","day":"01","year":"2021","isi":1,"has_accepted_license":"1","oa":1,"publisher":"Springer Nature","quality_controlled":"1"},{"volume":373,"issue":"8","ec_funded":1,"publication_identifier":{"eissn":["10886850"],"issn":["00029947"]},"publication_status":"published","language":[{"iso":"eng"}],"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.00859"}],"month":"08","intvolume":" 373","abstract":[{"lang":"eng","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))."}],"oa_version":"Preprint","department":[{"_id":"LaEr"}],"date_updated":"2023-08-17T14:31:03Z","ddc":["515"],"article_type":"original","type":"journal_article","status":"public","keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"_id":"7389","page":"5855-5883","doi":"10.1090/tran/8113","date_published":"2020-08-01T00:00:00Z","date_created":"2020-01-29T10:20:46Z","isi":1,"year":"2020","day":"01","publication":"Transactions of the American Mathematical Society","quality_controlled":"1","publisher":"American Mathematical Society","oa":1,"author":[{"first_name":"Gyorgy Pal","last_name":"Geher","full_name":"Geher, Gyorgy Pal"},{"first_name":"Tamas","last_name":"Titkos","full_name":"Titkos, Tamas"},{"orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel"}],"external_id":{"isi":["000551418100018"],"arxiv":["2002.00859"]},"article_processing_charge":"No","title":"Isometric study of Wasserstein spaces - the real line","citation":{"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","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","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.","short":"G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society 373 (2020) 5855–5883.","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425"}]},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"short":"L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020).","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.","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","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.","ista":"Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 278(12), 108507.","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."},"title":"Local laws for polynomials of Wigner matrices","article_processing_charge":"No","external_id":{"isi":["000522798900001"],"arxiv":["1804.11340"]},"author":[{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"},{"id":"4D902E6A-F248-11E8-B48F-1D18A9856A87","first_name":"Yuriy","last_name":"Nemish","full_name":"Nemish, Yuriy","orcid":"0000-0002-7327-856X"}],"article_number":"108507","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"publication":"Journal of Functional Analysis","day":"01","year":"2020","isi":1,"date_created":"2020-02-23T23:00:36Z","doi":"10.1016/j.jfa.2020.108507","date_published":"2020-07-01T00:00:00Z","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","oa":1,"publisher":"Elsevier","quality_controlled":"1","date_updated":"2023-08-18T06:36:10Z","department":[{"_id":"LaEr"}],"_id":"7512","status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["10960783"],"issn":["00221236"]},"ec_funded":1,"volume":278,"issue":"12","oa_version":"Preprint","abstract":[{"lang":"eng","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."}],"intvolume":" 278","month":"07","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.11340"}],"scopus_import":"1"},{"quality_controlled":"1","publisher":"Springer Nature","oa":1,"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.","date_published":"2020-08-01T00:00:00Z","doi":"10.1007/s11005-020-01282-0","date_created":"2020-03-25T15:57:48Z","page":"2039-2052","day":"01","publication":"Letters in Mathematical Physics","isi":1,"year":"2020","project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"title":"Quantum Hellinger distances revisited","author":[{"full_name":"Pitrik, Jozsef","last_name":"Pitrik","first_name":"Jozsef"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel","last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel"}],"external_id":{"isi":["000551556000002"],"arxiv":["1903.10455"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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","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","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.","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.","ista":"Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 110(8), 2039–2052.","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."},"month":"08","intvolume":" 110","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.10455"}],"oa_version":"Preprint","abstract":[{"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. ","lang":"eng"}],"issue":"8","volume":110,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"publication_status":"published","status":"public","type":"journal_article","article_type":"original","_id":"7618","department":[{"_id":"LaEr"}],"date_updated":"2023-08-18T10:17:26Z"},{"doi":"10.1007/s11854-020-0135-2","date_published":"2020-11-01T00:00:00Z","date_created":"2021-02-07T23:01:15Z","page":"323-348","day":"01","publication":"Journal d'Analyse Mathematique","isi":1,"year":"2020","quality_controlled":"1","publisher":"Springer Nature","oa":1,"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.","title":"On the support of the free additive convolution","author":[{"last_name":"Bao","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin"}],"article_processing_charge":"No","external_id":{"arxiv":["1804.11199"],"isi":["000611879400008"]},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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","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","short":"Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348.","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.","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.","ista":"Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 323–348.","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."},"project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"volume":142,"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["00217670"],"eissn":["15658538"]},"publication_status":"published","month":"11","intvolume":" 142","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1804.11199","open_access":"1"}],"oa_version":"Preprint","abstract":[{"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].","lang":"eng"}],"department":[{"_id":"LaEr"}],"date_updated":"2023-08-24T11:16:03Z","status":"public","article_type":"original","type":"journal_article","_id":"9104"},{"department":[{"_id":"LaEr"}],"date_updated":"2023-08-24T14:08:42Z","keyword":["Analysis"],"status":"public","article_type":"original","type":"journal_article","_id":"10862","ec_funded":1,"volume":279,"issue":"7","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0022-1236"]},"intvolume":" 279","month":"10","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01597"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"title":"Spectral rigidity for addition of random matrices at the regular edge","article_processing_charge":"No","external_id":{"arxiv":["1708.01597"],"isi":["000559623200009"]},"author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang","last_name":"Bao","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"full_name":"Schnelli, Kevin","last_name":"Schnelli","first_name":"Kevin"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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."},"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"article_number":"108639","date_created":"2022-03-18T10:18:59Z","doi":"10.1016/j.jfa.2020.108639","date_published":"2020-10-15T00:00:00Z","publication":"Journal of Functional Analysis","day":"15","year":"2020","isi":1,"oa":1,"quality_controlled":"1","publisher":"Elsevier","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804."},{"date_updated":"2023-08-28T08:38:48Z","department":[{"_id":"LaEr"}],"_id":"6488","status":"public","article_type":"original","type":"journal_article","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["20103263"],"eissn":["20103271"]},"ec_funded":1,"issue":"3","volume":9,"oa_version":"Preprint","abstract":[{"lang":"eng","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."}],"intvolume":" 9","month":"07","main_file_link":[{"url":"https://arxiv.org/abs/1806.08751","open_access":"1"}],"scopus_import":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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.","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.","short":"G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).","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","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","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."},"title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","article_processing_charge":"No","external_id":{"arxiv":["1806.08751"],"isi":["000547464400001"]},"author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"article_number":"2050006","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"publication":"Random Matrices: Theory and Application","day":"01","year":"2020","isi":1,"date_created":"2019-05-26T21:59:14Z","date_published":"2020-07-01T00:00:00Z","doi":"10.1142/S2010326320500069","oa":1,"publisher":"World Scientific Publishing","quality_controlled":"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)."}],"month":"09","intvolume":" 378","scopus_import":"1","file":[{"date_created":"2020-11-18T11:14:37Z","file_name":"2020_CommMathPhysics_Erdoes.pdf","date_updated":"2020-11-18T11:14:37Z","file_size":2904574,"creator":"dernst","file_id":"8771","checksum":"c3a683e2afdcea27afa6880b01e53dc2","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"publication_status":"published","volume":378,"related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"}]},"ec_funded":1,"_id":"6185","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":["530","510"],"date_updated":"2023-09-07T12:54:12Z","file_date_updated":"2020-11-18T11:14:37Z","department":[{"_id":"LaEr"}],"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.","publisher":"Springer Nature","quality_controlled":"1","oa":1,"day":"01","publication":"Communications in Mathematical Physics","isi":1,"has_accepted_license":"1","year":"2020","doi":"10.1007/s00220-019-03657-4","date_published":"2020-09-01T00:00:00Z","date_created":"2019-03-28T10:21:15Z","page":"1203-1278","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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","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","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.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.","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.","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."},"title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","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","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["1809.03971"],"isi":["000529483000001"]}},{"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"},{"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":"Yes","title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","citation":{"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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","page":"1421-1539","doi":"10.4171/dm/780","date_published":"2020-09-01T00:00:00Z","date_created":"2023-12-18T10:37:43Z","has_accepted_license":"1","year":"2020","day":"01","publication":"Documenta Mathematica","quality_controlled":"1","publisher":"EMS Press","oa":1,"department":[{"_id":"LaEr"}],"file_date_updated":"2023-12-18T10:42:32Z","date_updated":"2023-12-18T10:46:09Z","ddc":["510"],"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":["General Mathematics"],"_id":"14694","related_material":{"record":[{"status":"public","id":"6183","relation":"earlier_version"}]},"volume":25,"publication_identifier":{"issn":["1431-0635"],"eissn":["1431-0643"]},"publication_status":"published","file":[{"success":1,"file_id":"14695","checksum":"12aacc1d63b852ff9a51c1f6b218d4a6","content_type":"application/pdf","relation":"main_file","access_level":"open_access","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"}],"language":[{"iso":"eng"}],"month":"09","intvolume":" 25","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"}],"oa_version":"Published Version"},{"oa_version":"Preprint","abstract":[{"lang":"eng","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."}],"month":"03","intvolume":" 48","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1804.07744","open_access":"1"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0091-1798"]},"publication_status":"published","related_material":{"record":[{"relation":"dissertation_contains","status":"public","id":"149"},{"relation":"dissertation_contains","id":"6179","status":"public"}]},"issue":"2","volume":48,"ec_funded":1,"_id":"6184","status":"public","article_type":"original","type":"journal_article","date_updated":"2024-02-22T14:34:33Z","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","oa":1,"day":"01","publication":"Annals of Probability","isi":1,"year":"2020","date_published":"2020-03-01T00:00:00Z","doi":"10.1214/19-AOP1379","date_created":"2019-03-28T09:20:08Z","page":"963-1001","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","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","short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001.","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."},"title":"Correlated random matrices: Band rigidity and edge universality","author":[{"first_name":"Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","full_name":"Alt, Johannes"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","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"}],"article_processing_charge":"No","external_id":{"isi":["000528269100013"],"arxiv":["1804.07744"]}},{"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2690-1005","2690-0998"]},"publication_status":"published","volume":1,"issue":"1","ec_funded":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)."}],"month":"11","intvolume":" 1","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1908.01653"}],"date_updated":"2024-03-04T10:33:15Z","department":[{"_id":"LaEr"}],"_id":"15063","status":"public","keyword":["General Medicine"],"article_type":"original","type":"journal_article","day":"16","publication":"Probability and Mathematical Physics","year":"2020","doi":"10.2140/pmp.2020.1.101","date_published":"2020-11-16T00:00:00Z","date_created":"2024-03-04T10:27:57Z","page":"101-146","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","quality_controlled":"1","publisher":"Mathematical Sciences Publishers","oa":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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","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.","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.","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."},"title":"Optimal lower bound on the least singular value of the shifted Ginibre ensemble","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"article_processing_charge":"No","external_id":{"arxiv":["1908.01653"]},"project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}]},{"_id":"15079","type":"journal_article","article_type":"original","status":"public","date_updated":"2024-03-12T12:25:18Z","citation":{"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.","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."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","article_processing_charge":"No","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Götze","full_name":"Götze, Friedrich","first_name":"Friedrich"},{"first_name":"Alice","full_name":"Guionnet, Alice","last_name":"Guionnet"}],"title":"Random matrices","department":[{"_id":"LaEr"}],"abstract":[{"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.","lang":"eng"}],"oa_version":"None","quality_controlled":"1","publisher":"European Mathematical Society","intvolume":" 16","month":"11","publication_status":"published","year":"2020","publication_identifier":{"issn":["1660-8933"]},"language":[{"iso":"eng"}],"publication":"Oberwolfach Reports","day":"19","page":"3459-3527","date_created":"2024-03-05T07:54:44Z","date_published":"2020-11-19T00:00:00Z","doi":"10.4171/owr/2019/56","issue":"4","volume":16},{"status":"public","conference":{"start_date":"2019-01-28","location":"Kyoto, Japan","end_date":"2019-01-30","name":"Research on isometries as preserver problems and related topics"},"type":"conference","_id":"7035","department":[{"_id":"LaEr"}],"title":"Dirac masses and isometric rigidity","article_processing_charge":"No","author":[{"first_name":"Gyorgy Pal","full_name":"Geher, Gyorgy Pal","last_name":"Geher"},{"first_name":"Tamas","full_name":"Titkos, Tamas","last_name":"Titkos"},{"orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","first_name":"Daniel"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","date_updated":"2021-01-12T08:11:33Z","citation":{"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.","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.","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.","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.","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.","short":"G.P. Geher, T. Titkos, D. Virosztek, in:, Kyoto RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41."},"intvolume":" 2125","month":"01","main_file_link":[{"open_access":"1","url":"http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html"}],"oa":1,"quality_controlled":"1","publisher":"Research Institute for Mathematical Sciences, Kyoto University","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."}],"date_created":"2019-11-18T15:39:53Z","volume":2125,"date_published":"2019-01-30T00:00:00Z","page":"34-41","publication":"Kyoto RIMS Kôkyûroku","language":[{"iso":"eng"}],"day":"30","year":"2019","publication_status":"published"},{"article_number":"34","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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.","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.","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.","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.","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."},"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","last_name":"Nejjar","full_name":"Nejjar, Peter"},{"full_name":"Vuletíc, Mirjana","last_name":"Vuletíc","first_name":"Mirjana"}],"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","oa":1,"quality_controlled":"1","publisher":"Formal Power Series and Algebraic Combinatorics","publication":"Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics","day":"01","year":"2019","date_created":"2020-07-26T22:01:04Z","date_published":"2019-07-01T00:00:00Z","_id":"8175","status":"public","conference":{"name":"FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics","location":"Ljubljana, Slovenia","end_date":"2019-07-05","start_date":"2019-07-01"},"type":"conference","date_updated":"2021-01-12T08:17:18Z","department":[{"_id":"LaEr"}],"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."}],"month":"07","main_file_link":[{"url":"https://arxiv.org/abs/1902.08750","open_access":"1"}],"scopus_import":"1","language":[{"iso":"eng"}],"publication_status":"published","ec_funded":1},{"date_created":"2018-12-11T11:46:17Z","date_published":"2019-09-01T00:00:00Z","doi":"10.1016/j.laa.2018.03.002","page":"67-78","publication":"Linear Algebra and Its Applications","day":"01","year":"2019","isi":1,"oa":1,"quality_controlled":"1","publisher":"Elsevier","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)","title":"Jointly convex quantum Jensen divergences","external_id":{"arxiv":["1712.05324"],"isi":["000470955300005"]},"article_processing_charge":"No","author":[{"orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","last_name":"Virosztek","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"7424","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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.","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","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","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."},"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"ec_funded":1,"volume":576,"language":[{"iso":"eng"}],"publication_status":"published","intvolume":" 576","month":"09","main_file_link":[{"url":"https://arxiv.org/abs/1712.05324","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"lang":"eng","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."}],"department":[{"_id":"LaEr"}],"date_updated":"2023-08-24T14:31:47Z","status":"public","article_type":"original","type":"journal_article","_id":"405"},{"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"title":"Stability of the matrix Dyson equation and random matrices with correlations","external_id":{"isi":["000459396500007"]},"article_processing_charge":"Yes (via OA deal)","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","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger"}],"publist_id":"7394","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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.","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","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.","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."},"oa":1,"publisher":"Springer","quality_controlled":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\n","date_created":"2018-12-11T11:46:25Z","doi":"10.1007/s00440-018-0835-z","date_published":"2019-02-01T00:00:00Z","page":"293–373","publication":"Probability Theory and Related Fields","day":"01","year":"2019","isi":1,"has_accepted_license":"1","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":"429","file_date_updated":"2020-07-14T12:46:26Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2023-08-24T14:39:00Z","intvolume":" 173","month":"02","scopus_import":"1","oa_version":"Published Version","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"}],"ec_funded":1,"issue":"1-2","volume":173,"language":[{"iso":"eng"}],"file":[{"date_updated":"2020-07-14T12:46:26Z","file_size":1201840,"creator":"dernst","date_created":"2018-12-17T16:12:08Z","file_name":"2018_ProbTheory_Ajanki.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"f9354fa5c71f9edd17132588f0dc7d01","file_id":"5720"}],"publication_status":"published","publication_identifier":{"issn":["01788051"],"eissn":["14322064"]}},{"title":"Singular analytic linear cocycles with negative infinite Lyapunov exponents","external_id":{"isi":["000459725600012"],"arxiv":["1601.06118"]},"article_processing_charge":"No","author":[{"last_name":"Sadel","full_name":"Sadel, Christian","orcid":"0000-0001-8255-3968","first_name":"Christian","id":"4760E9F8-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Disheng","last_name":"Xu","full_name":"Xu, Disheng"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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","short":"C. Sadel, D. Xu, Ergodic Theory and Dynamical Systems 39 (2019) 1082–1098.","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."},"project":[{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7","_id":"25681D80-B435-11E9-9278-68D0E5697425"}],"date_created":"2019-03-10T22:59:18Z","date_published":"2019-04-01T00:00:00Z","doi":"10.1017/etds.2017.52","page":"1082-1098","publication":"Ergodic Theory and Dynamical Systems","day":"01","year":"2019","isi":1,"oa":1,"publisher":"Cambridge University Press","quality_controlled":"1","department":[{"_id":"LaEr"}],"date_updated":"2023-08-25T08:03:30Z","status":"public","type":"journal_article","_id":"6086","ec_funded":1,"volume":39,"issue":"4","language":[{"iso":"eng"}],"publication_status":"published","intvolume":" 39","month":"04","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1601.06118"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"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.","lang":"eng"}]},{"title":"Local single ring theorem on optimal scale","author":[{"first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","last_name":"Bao","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin"}],"external_id":{"arxiv":["1612.05920"],"isi":["000466616100003"]},"article_processing_charge":"No","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","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.","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","short":"Z. Bao, L. Erdös, K. Schnelli, Annals of Probability 47 (2019) 1270–1334.","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.","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."},"project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"doi":"10.1214/18-AOP1284","date_published":"2019-05-01T00:00:00Z","date_created":"2019-06-02T21:59:13Z","page":"1270-1334","day":"01","publication":"Annals of Probability","isi":1,"year":"2019","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"department":[{"_id":"LaEr"}],"date_updated":"2023-08-28T09:32:29Z","status":"public","type":"journal_article","_id":"6511","volume":47,"issue":"3","ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["00911798"]},"publication_status":"published","month":"05","intvolume":" 47","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1612.05920","open_access":"1"}],"oa_version":"Preprint","abstract":[{"lang":"eng","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)."}]},{"department":[{"_id":"LaEr"}],"date_updated":"2023-08-29T07:18:50Z","article_type":"original","type":"journal_article","status":"public","_id":"6843","ec_funded":1,"volume":480,"issue":"2","publication_status":"published","publication_identifier":{"eissn":["10960813"],"issn":["0022247X"]},"language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/1809.01101","open_access":"1"}],"scopus_import":"1","intvolume":" 480","month":"12","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. 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","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of Mathematical Analysis and Applications 480 (2019).","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.","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.","ista":"Gehér GP, Titkos T, Virosztek D. 2019. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 480(2), 123435.","chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” Journal of Mathematical Analysis and Applications. Elsevier, 2019. https://doi.org/10.1016/j.jmaa.2019.123435."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"article_number":"123435","date_created":"2019-09-01T22:01:01Z","date_published":"2019-12-15T00:00:00Z","doi":"10.1016/j.jmaa.2019.123435","year":"2019","isi":1,"publication":"Journal of Mathematical Analysis and Applications","day":"15","oa":1,"publisher":"Elsevier","quality_controlled":"1"},{"_id":"7423","status":"public","type":"journal_article","article_type":"original","date_updated":"2023-09-06T14:58:39Z","department":[{"_id":"LaEr"}],"oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"intvolume":" 55","month":"02","main_file_link":[{"url":"https://arxiv.org/abs/1704.05224","open_access":"1"}],"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["0246-0203"]},"issue":"1","volume":55,"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.","short":"G. Akemann, T. Checinski, D. Liu, E. Strahov, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55 (2019) 441–479.","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.","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."},"title":"Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles","article_processing_charge":"No","external_id":{"arxiv":["1704.05224"],"isi":["000456070200013"]},"author":[{"first_name":"Gernot","full_name":"Akemann, Gernot","last_name":"Akemann"},{"full_name":"Checinski, Tomasz","last_name":"Checinski","first_name":"Tomasz"},{"full_name":"Liu, Dangzheng","last_name":"Liu","id":"2F947E34-F248-11E8-B48F-1D18A9856A87","first_name":"Dangzheng"},{"last_name":"Strahov","full_name":"Strahov, Eugene","first_name":"Eugene"}],"oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","publication":"Annales de l'Institut Henri Poincaré, Probabilités et Statistiques","day":"01","year":"2019","isi":1,"date_created":"2020-01-30T10:36:50Z","date_published":"2019-02-01T00:00:00Z","doi":"10.1214/18-aihp888","page":"441-479"},{"file_date_updated":"2020-07-14T12:47:22Z","department":[{"_id":"LaEr"}],"date_updated":"2023-09-07T12:54:12Z","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)"},"article_type":"original","type":"journal_article","status":"public","_id":"6182","ec_funded":1,"related_material":{"record":[{"status":"public","id":"6179","relation":"dissertation_contains"}]},"volume":7,"publication_status":"published","publication_identifier":{"eissn":["20505094"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2019_Forum_Erdoes.pdf","date_created":"2019-09-17T14:24:13Z","file_size":1520344,"date_updated":"2020-07-14T12:47:22Z","creator":"dernst","checksum":"933a472568221c73b2c3ce8c87bf6d15","file_id":"6883","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"scopus_import":"1","intvolume":" 7","month":"03","abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","article_processing_charge":"No","external_id":{"arxiv":["1705.10661"],"isi":["000488847100001"]},"author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","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":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"title":"Random matrices with slow correlation decay","citation":{"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.","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.","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.","ista":"Erdös L, Krüger TH, Schröder DJ. 2019. Random matrices with slow correlation decay. Forum of Mathematics, Sigma. 7, e8."},"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"}],"article_number":"e8","date_created":"2019-03-28T09:05:23Z","doi":"10.1017/fms.2019.2","date_published":"2019-03-26T00:00:00Z","year":"2019","has_accepted_license":"1","isi":1,"publication":"Forum of Mathematics, Sigma","day":"26","oa":1,"publisher":"Cambridge University Press","quality_controlled":"1"},{"status":"public","type":"journal_article","article_type":"original","_id":"6186","department":[{"_id":"LaEr"}],"date_updated":"2023-09-07T12:54:12Z","month":"10","intvolume":" 1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1811.04055"}],"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"}],"issue":"4","volume":1,"related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"}]},"ec_funded":1,"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"publication_status":"published","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385","name":"International IST Doctoral Program"}],"title":"Cusp universality for random matrices, II: The real symmetric case","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","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"},{"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":{"arxiv":["1811.04055"]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"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.","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","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","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.","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."},"quality_controlled":"1","publisher":"MSP","oa":1,"doi":"10.2140/paa.2019.1.615","date_published":"2019-10-12T00:00:00Z","date_created":"2019-03-28T10:21:17Z","page":"615–707","day":"12","publication":"Pure and Applied Analysis ","year":"2019"},{"intvolume":" 9","month":"03","main_file_link":[{"url":"https://arxiv.org/abs/1701.02956","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"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.","lang":"eng"}],"issue":"3","volume":9,"language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["1664-039X"]},"keyword":["Random Schrödinger operators","spectral shift function","Anderson orthogonality"],"status":"public","article_type":"original","type":"journal_article","_id":"10879","department":[{"_id":"LaEr"}],"date_updated":"2023-09-08T11:35:31Z","oa":1,"quality_controlled":"1","publisher":"European Mathematical Society Publishing House","acknowledgement":"M.G. was supported by the DFG under grant GE 2871/1-1.","date_created":"2022-03-18T12:36:42Z","doi":"10.4171/jst/267","date_published":"2019-03-01T00:00:00Z","page":"921-965","publication":"Journal of Spectral Theory","day":"01","year":"2019","isi":1,"title":"Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function","external_id":{"isi":["000484709400006"],"arxiv":["1701.02956"]},"article_processing_charge":"No","author":[{"first_name":"Adrian M","id":"317CB464-F248-11E8-B48F-1D18A9856A87","full_name":"Dietlein, Adrian M","last_name":"Dietlein"},{"full_name":"Gebert, Martin","last_name":"Gebert","first_name":"Martin"},{"first_name":"Peter","last_name":"Müller","full_name":"Müller, Peter"}],"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.","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","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"}}]