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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","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_updated":"2023-08-02T13:44:32Z","type":"journal_article","article_type":"original","keyword":["mathematical physics","statistical and nonlinear physics"],"status":"public","_id":"10600","date_created":"2022-01-03T12:19:48Z","date_published":"2022-01-03T00:00:00Z","doi":"10.1063/5.0051632","year":"2022","isi":1,"publication":"Journal of Mathematical Physics","day":"03","oa":1,"quality_controlled":"1","publisher":"AIP Publishing","acknowledgement":"J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331.","external_id":{"isi":["000739446000009"],"arxiv":["2012.15238"]},"article_processing_charge":"No","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","citation":{"chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” Journal of Mathematical Physics. 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We call this a strong version of the local perturbations perturb locally (LPPL) principle which is known to hold for much more general gapped systems, but only for perturbations that do not close the spectral gap of the Hamiltonian. We also extend this strong LPPL-principle to Hamiltonians that have the appropriate structure of gapped on-site terms and weak interactions only locally in some region of space. While our results are technically corollaries to a theorem of Yarotsky, we expect that the paradigm of systems with a locally gapped ground state that is completely insensitive to the form of the Hamiltonian elsewhere extends to other situations and has important physical consequences.","lang":"eng"}],"oa_version":"Published Version","ec_funded":1,"volume":112,"issue":"1","publication_status":"published","publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"language":[{"iso":"eng"}],"file":[{"creator":"cchlebak","date_updated":"2022-01-19T09:41:14Z","file_size":357547,"date_created":"2022-01-19T09:41:14Z","file_name":"2022_LettersMathPhys_Henheik.pdf","access_level":"open_access","relation":"main_file","content_type":"application/pdf","checksum":"7e8e69b76e892c305071a4736131fe18","file_id":"10647","success":1}],"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}],"article_number":"9","article_processing_charge":"No","external_id":{"isi":["000744930400001"],"arxiv":["2106.13780"]},"author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"last_name":"Teufel","full_name":"Teufel, Stefan","first_name":"Stefan"},{"last_name":"Wessel","full_name":"Wessel, Tom","first_name":"Tom"}],"title":"Local stability of ground states in locally gapped and weakly interacting quantum spin systems","citation":{"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.","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.","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.","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)."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"publisher":"Springer Nature","quality_controlled":"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.","date_created":"2022-01-18T16:18:25Z","doi":"10.1007/s11005-021-01494-y","date_published":"2022-01-18T00:00:00Z","year":"2022","has_accepted_license":"1","isi":1,"publication":"Letters in Mathematical Physics","day":"18"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.","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.","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. 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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,"ddc":["510"],"date_updated":"2023-08-02T13:53:11Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-19T09:27:43Z","_id":"10643","status":"public","keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"87592a755adcef22ea590a99dc728dd3","file_id":"10646","success":1,"date_updated":"2022-01-19T09:27:43Z","file_size":705323,"creator":"cchlebak","date_created":"2022-01-19T09:27:43Z","file_name":"2022_ForumMathSigma_Henheik.pdf"}],"language":[{"iso":"eng"}],"publication_identifier":{"eissn":["2050-5094"]},"publication_status":"published","volume":10,"ec_funded":1,"oa_version":"Published Version","abstract":[{"text":"We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.\r\n\r\n","lang":"eng"}],"month":"01","intvolume":" 10"},{"publication_identifier":{"issn":["1385-0172"],"eissn":["1572-9656"]},"publication_status":"published","file":[{"date_created":"2022-01-14T07:27:45Z","file_name":"2022_MathPhyAnalGeo_Henheik.pdf","date_updated":"2022-01-14T07:27:45Z","file_size":505804,"creator":"cchlebak","file_id":"10624","checksum":"d44f8123a52592a75b2c3b8ee2cd2435","success":1,"content_type":"application/pdf","access_level":"open_access","relation":"main_file"}],"language":[{"iso":"eng"}],"issue":"1","volume":25,"ec_funded":1,"abstract":[{"text":"We investigate the BCS critical temperature Tc in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of Tc at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"01","intvolume":" 25","date_updated":"2023-08-02T13:51:52Z","ddc":["514"],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-14T07:27:45Z","_id":"10623","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","keyword":["geometry and topology","mathematical physics"],"isi":1,"has_accepted_license":"1","year":"2022","day":"11","publication":"Mathematical Physics, Analysis and Geometry","doi":"10.1007/s11040-021-09415-0","date_published":"2022-01-11T00:00:00Z","date_created":"2022-01-13T15:40:53Z","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.","quality_controlled":"1","publisher":"Springer Nature","oa":1,"citation":{"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.","ista":"Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3.","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.","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","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","ieee":"S. J. Henheik, “The BCS critical temperature at high density,” Mathematical Physics, Analysis and Geometry, vol. 25, no. 1. Springer Nature, 2022.","short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022)."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"arxiv":["2106.02015"],"isi":["000741387600001"]},"title":"The BCS critical temperature at high density","article_number":"3","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"}]},{"publication_identifier":{"issn":["0022-1236"],"eissn":["1096-0783"]},"publication_status":"published","file":[{"checksum":"b75fdad606ab507dc61109e0907d86c0","file_id":"11690","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf","date_created":"2022-07-29T07:22:08Z","file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","creator":"dernst","date_updated":"2022-07-29T07:22:08Z","file_size":652573}],"language":[{"iso":"eng"}],"issue":"8","volume":282,"abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","scopus_import":"1","month":"04","intvolume":" 282","date_updated":"2023-08-02T14:12:35Z","ddc":["500"],"department":[{"_id":"LaEr"}],"file_date_updated":"2022-07-29T07:22:08Z","_id":"10732","type":"journal_article","article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"status":"public","has_accepted_license":"1","isi":1,"year":"2022","day":"15","publication":"Journal of Functional Analysis","date_published":"2022-04-15T00:00:00Z","doi":"10.1016/j.jfa.2022.109394","date_created":"2022-02-06T23:01:30Z","acknowledgement":"We compute the deterministic approximation of products of Sobolev functions of large Wigner matrices W and provide an optimal error bound on their fluctuation with very high probability. This generalizes Voiculescu's seminal theorem from polynomials to general Sobolev functions, as well as from tracial quantities to individual matrix elements. Applying the result to for large t, we obtain a precise decay rate for the overlaps of several deterministic matrices with temporally well separated Heisenberg time evolutions; thus we demonstrate the thermalisation effect of the unitary group generated by Wigner matrices.","quality_controlled":"1","publisher":"Elsevier","oa":1,"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.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Thermalisation for Wigner matrices. Journal of Functional Analysis. Elsevier. https://doi.org/10.1016/j.jfa.2022.109394","ama":"Cipolloni G, Erdös L, Schröder DJ. Thermalisation for Wigner matrices. Journal of Functional Analysis. 2022;282(8). doi:10.1016/j.jfa.2022.109394","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"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":{"isi":["000781239100004"],"arxiv":["2102.09975"]},"title":"Thermalisation for Wigner matrices","article_number":"109394"},{"volume":11,"issue":"4","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"issn":["2010-3263"],"eissn":["2010-3271"]},"intvolume":" 11","month":"10","main_file_link":[{"open_access":"1","url":" https://doi.org/10.48550/arXiv.2103.03906"}],"scopus_import":"1","oa_version":"Preprint","abstract":[{"text":"We consider a correlated NxN Hermitian random matrix with a polynomially decaying metric correlation structure. By calculating the trace of the moments of the matrix and using the summable decay of the cumulants, we show that its operator norm is stochastically dominated by one.","lang":"eng"}],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"date_updated":"2023-08-03T06:32:22Z","keyword":["Discrete Mathematics and Combinatorics","Statistics","Probability and Uncertainty","Statistics and Probability","Algebra and Number Theory"],"status":"public","article_type":"original","type":"journal_article","_id":"11135","date_created":"2022-04-08T07:11:12Z","date_published":"2022-10-01T00:00:00Z","doi":"10.1142/s2010326322500368","publication":"Random Matrices: Theory and Applications","day":"01","year":"2022","isi":1,"oa":1,"quality_controlled":"1","publisher":"World Scientific","title":"On the operator norm of a Hermitian random matrix with correlated entries","article_processing_charge":"No","external_id":{"isi":["000848873800001"],"arxiv":["2103.03906"]},"author":[{"id":"e796e4f9-dc8d-11ea-abe3-97e26a0323e9","first_name":"Jana","full_name":"Reker, Jana","last_name":"Reker"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"short":"J. Reker, Random Matrices: Theory and Applications 11 (2022).","ieee":"J. Reker, “On the operator norm of a Hermitian random matrix with correlated entries,” Random Matrices: Theory and Applications, vol. 11, no. 4. World Scientific, 2022.","apa":"Reker, J. (2022). On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. World Scientific. https://doi.org/10.1142/s2010326322500368","ama":"Reker J. On the operator norm of a Hermitian random matrix with correlated entries. Random Matrices: Theory and Applications. 2022;11(4). doi:10.1142/s2010326322500368","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."},"article_number":"2250036"},{"ec_funded":1,"volume":393,"publication_status":"published","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"11726","checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","file_size":1141462,"date_updated":"2022-08-05T06:01:13Z","creator":"dernst","file_name":"2022_CommunMathPhys_Schnelli.pdf","date_created":"2022-08-05T06:01:13Z"}],"scopus_import":"1","intvolume":" 393","month":"07","abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","file_date_updated":"2022-08-05T06:01:13Z","department":[{"_id":"LaEr"}],"date_updated":"2023-08-03T06:34:24Z","ddc":["510"],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"type":"journal_article","article_type":"original","status":"public","_id":"11332","page":"839-907","date_created":"2022-04-24T22:01:44Z","date_published":"2022-07-01T00:00:00Z","doi":"10.1007/s00220-022-04377-y","year":"2022","isi":1,"has_accepted_license":"1","publication":"Communications in Mathematical Physics","day":"01","oa":1,"publisher":"Springer Nature","quality_controlled":"1","acknowledgement":"Kevin Schnelli is supported in parts by the Swedish Research Council Grant VR-2017-05195, and the Knut and Alice Wallenberg Foundation. Yuanyuan Xu is supported by the Swedish Research Council Grant VR-2017-05195 and the ERC Advanced Grant “RMTBeyond” No. 101020331.","article_processing_charge":"No","external_id":{"isi":["000782737200001"],"arxiv":["2102.04330"]},"author":[{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin"},{"first_name":"Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","last_name":"Xu","full_name":"Xu, Yuanyuan"}],"title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","citation":{"chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical Physics. Springer Nature, 2022. https://doi.org/10.1007/s00220-022-04377-y.","ista":"Schnelli K, Xu Y. 2022. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 393, 839–907.","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” Communications in Mathematical Physics, vol. 393, Springer Nature, 2022, pp. 839–907, doi:10.1007/s00220-022-04377-y.","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.","apa":"Schnelli, K., & Xu, Y. (2022). Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-022-04377-y","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. Communications in Mathematical Physics. 2022;393:839-907. doi:10.1007/s00220-022-04377-y"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331"}]},{"author":[{"orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös"},{"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":["2103.06730"],"isi":["000793963400005"]},"title":"Normal fluctuation in quantum ergodicity for Wigner matrices","citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” Annals of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/21-AOP1552.","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.","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","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","page":"984-1012","doi":"10.1214/21-AOP1552","date_published":"2022-05-01T00:00:00Z","date_created":"2022-05-29T22:01:53Z","isi":1,"year":"2022","day":"01","publication":"Annals of Probability","quality_controlled":"1","publisher":"Institute of Mathematical Statistics","oa":1,"acknowledgement":"L.E. would like to thank Zhigang Bao for many illuminating discussions in an early stage of this research. The authors are also grateful to Paul Bourgade for his comments on the manuscript and the anonymous referee for several useful suggestions.","department":[{"_id":"LaEr"}],"date_updated":"2023-08-03T07:16:53Z","type":"journal_article","article_type":"original","status":"public","_id":"11418","volume":50,"issue":"3","publication_identifier":{"eissn":["2168-894X"],"issn":["0091-1798"]},"publication_status":"published","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"month":"05","intvolume":" 50","abstract":[{"text":"We consider the quadratic form of a general high-rank deterministic matrix on the eigenvectors of an N×N\r\nWigner matrix and prove that it has Gaussian fluctuation for each bulk eigenvector in the large N limit. The proof is a combination of the energy method for the Dyson Brownian motion inspired by Marcinek and Yau (2021) and our recent multiresolvent local laws (Comm. Math. Phys. 388 (2021) 1005–1048).","lang":"eng"}],"oa_version":"Preprint"},{"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."}],"intvolume":" 63","month":"12","scopus_import":"1","language":[{"iso":"eng"}],"file":[{"date_created":"2023-01-20T11:58:59Z","file_name":"2022_JourMathPhysics_Henheik.pdf","creator":"dernst","date_updated":"2023-01-20T11:58:59Z","file_size":5436804,"file_id":"12327","checksum":"5150287295e0ce4f12462c990744d65d","success":1,"access_level":"open_access","relation":"main_file","content_type":"application/pdf"}],"publication_status":"published","publication_identifier":{"issn":["0022-2488"]},"ec_funded":1,"issue":"12","volume":63,"_id":"12110","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"],"date_updated":"2023-08-03T14:12:01Z","file_date_updated":"2023-01-20T11:58:59Z","department":[{"_id":"LaEr"}],"acknowledgement":"J.H. gratefully acknowledges the partial financial support by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n","oa":1,"quality_controlled":"1","publisher":"AIP Publishing","publication":"Journal of Mathematical Physics","day":"01","year":"2022","has_accepted_license":"1","isi":1,"date_created":"2023-01-08T23:00:53Z","doi":"10.1063/5.0104675","date_published":"2022-12-01T00:00:00Z","article_number":"122302","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":{"mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” Journal of Mathematical Physics, vol. 63, no. 12, 122302, AIP Publishing, 2022, doi:10.1063/5.0104675.","short":"S.J. Henheik, R. Tumulka, Journal of Mathematical Physics 63 (2022).","ieee":"S. J. Henheik and R. Tumulka, “Interior-boundary conditions for the Dirac equation at point sources in three dimensions,” Journal of Mathematical Physics, vol. 63, no. 12. AIP Publishing, 2022.","ama":"Henheik SJ, Tumulka R. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. 2022;63(12). doi:10.1063/5.0104675","apa":"Henheik, S. J., & Tumulka, R. (2022). Interior-boundary conditions for the Dirac equation at point sources in three dimensions. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0104675","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","external_id":{"isi":["000900748900002"]},"article_processing_charge":"No","author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"full_name":"Tumulka, Roderich","last_name":"Tumulka","first_name":"Roderich"}]},{"date_updated":"2023-08-04T09:00:35Z","ddc":["510"],"file_date_updated":"2023-01-24T10:02:40Z","department":[{"_id":"LaEr"}],"_id":"12148","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":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"status":"public","publication_status":"published","publication_identifier":{"issn":["2050-5094"]},"language":[{"iso":"eng"}],"file":[{"content_type":"application/pdf","access_level":"open_access","relation":"main_file","checksum":"94a049aeb1eea5497aa097712a73c400","file_id":"12356","success":1,"date_updated":"2023-01-24T10:02:40Z","file_size":817089,"creator":"dernst","date_created":"2023-01-24T10:02:40Z","file_name":"2022_ForumMath_Cipolloni.pdf"}],"ec_funded":1,"volume":10,"abstract":[{"lang":"eng","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."}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 10","month":"10","citation":{"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.","mla":"Cipolloni, Giorgio, et al. “Rank-Uniform Local Law for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 10, e96, Cambridge University Press, 2022, doi:10.1017/fms.2022.86.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2022.86","ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. Forum of Mathematics, Sigma. 2022;10. doi:10.1017/fms.2022.86","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Forum of Mathematics, Sigma 10 (2022).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” Forum of Mathematics, Sigma, vol. 10. Cambridge University Press, 2022."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000873719200001"]},"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","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"}],"title":"Rank-uniform local law for Wigner matrices","article_number":"e96","project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"year":"2022","isi":1,"has_accepted_license":"1","publication":"Forum of Mathematics, Sigma","day":"27","date_created":"2023-01-12T12:07:30Z","date_published":"2022-10-27T00:00:00Z","doi":"10.1017/fms.2022.86","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.","oa":1,"quality_controlled":"1","publisher":"Cambridge University Press"},{"article_number":"121101","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"citation":{"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.","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","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.","ista":"Henheik SJ, Wessel T. 2022. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 63(12), 121101.","chicago":"Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0123441."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000905776200001"],"arxiv":["2208.12220"]},"article_processing_charge":"No","author":[{"last_name":"Henheik","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","first_name":"Sven Joscha"},{"first_name":"Tom","full_name":"Wessel, Tom","last_name":"Wessel"}],"title":"On adiabatic theory for extended fermionic lattice systems","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","year":"2022","isi":1,"has_accepted_license":"1","publication":"Journal of Mathematical Physics","day":"01","date_created":"2023-01-15T23:00:52Z","doi":"10.1063/5.0123441","date_published":"2022-12-01T00:00:00Z","_id":"12184","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","status":"public","date_updated":"2023-08-04T09:14:57Z","ddc":["510"],"file_date_updated":"2023-01-27T07:10:52Z","department":[{"_id":"LaEr"}],"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"}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 63","month":"12","publication_status":"published","publication_identifier":{"issn":["0022-2488"]},"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"12410","checksum":"213b93750080460718c050e4967cfdb4","success":1,"creator":"dernst","date_updated":"2023-01-27T07:10:52Z","file_size":5251092,"date_created":"2023-01-27T07:10:52Z","file_name":"2022_JourMathPhysics_Henheik2.pdf"}],"ec_funded":1,"volume":63,"issue":"12"},{"title":"The isometry group of Wasserstein spaces: The Hilbertian case","article_processing_charge":"No","external_id":{"isi":["000854878500001"],"arxiv":["2102.02037"]},"author":[{"full_name":"Gehér, György Pál","last_name":"Gehér","first_name":"György Pál"},{"full_name":"Titkos, Tamás","last_name":"Titkos","first_name":"Tamás"},{"first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","last_name":"Virosztek"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"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.","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.","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society 106 (2022) 3865–3894.","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “The isometry group of Wasserstein spaces: The Hilbertian case,” Journal of the London Mathematical Society, vol. 106, no. 4. Wiley, pp. 3865–3894, 2022.","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","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","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."},"project":[{"name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294","call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425"}],"date_created":"2023-01-16T09:46:13Z","date_published":"2022-09-18T00:00:00Z","doi":"10.1112/jlms.12676","page":"3865-3894","publication":"Journal of the London Mathematical Society","day":"18","year":"2022","isi":1,"oa":1,"quality_controlled":"1","publisher":"Wiley","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). ","department":[{"_id":"LaEr"}],"date_updated":"2023-08-04T09:24:17Z","keyword":["General Mathematics"],"status":"public","article_type":"original","type":"journal_article","_id":"12214","ec_funded":1,"volume":106,"issue":"4","language":[{"iso":"eng"}],"publication_status":"published","publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"intvolume":" 106","month":"09","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2102.02037","open_access":"1"}],"scopus_import":"1","oa_version":"Preprint","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"}]},{"date_created":"2023-01-16T09:50:26Z","doi":"10.1007/s00023-022-01188-8","date_published":"2022-11-01T00:00:00Z","page":"3981-4002","publication":"Annales Henri Poincaré","day":"01","year":"2022","has_accepted_license":"1","isi":1,"oa":1,"quality_controlled":"1","publisher":"Springer Nature","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.","title":"Density of small singular values of the shifted real Ginibre ensemble","external_id":{"isi":["000796323500001"]},"article_processing_charge":"No","author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"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":{"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.","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.","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","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","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” Annales Henri Poincaré, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022.","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."},"volume":23,"issue":"11","language":[{"iso":"eng"}],"file":[{"file_size":1333638,"date_updated":"2023-01-27T11:06:47Z","creator":"dernst","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","date_created":"2023-01-27T11:06:47Z","content_type":"application/pdf","relation":"main_file","access_level":"open_access","success":1,"file_id":"12424","checksum":"5582f059feeb2f63e2eb68197a34d7dc"}],"publication_status":"published","publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"intvolume":" 23","month":"11","scopus_import":"1","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"}],"department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-27T11:06:47Z","ddc":["510"],"date_updated":"2023-08-04T09:33:52Z","keyword":["Mathematical Physics","Nuclear and High Energy 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","_id":"12232"},{"date_updated":"2023-08-04T09:40:02Z","ddc":["510","530"],"department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-30T08:01:10Z","_id":"12243","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","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"status":"public","publication_status":"published","publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"language":[{"iso":"eng"}],"file":[{"creator":"dernst","file_size":7356807,"date_updated":"2023-01-30T08:01:10Z","file_name":"2022_JourMathPhysics_Cipolloni2.pdf","date_created":"2023-01-30T08:01:10Z","relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"checksum":"2db278ae5b07f345a7e3fec1f92b5c33","file_id":"12436"}],"ec_funded":1,"issue":"10","volume":63,"abstract":[{"lang":"eng","text":"We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. "}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 63","month":"10","citation":{"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.","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","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” Journal of Mathematical Physics, vol. 63, no. 10. AIP Publishing, 2022.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022).","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.","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"isi":["000869715800001"],"arxiv":["2206.04443"]},"article_processing_charge":"Yes (via OA deal)","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J"},{"last_name":"Xu","full_name":"Xu, Yuanyuan","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","first_name":"Yuanyuan"}],"title":"Directional extremal statistics for Ginibre eigenvalues","article_number":"103303","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"year":"2022","has_accepted_license":"1","isi":1,"publication":"Journal of Mathematical Physics","day":"14","date_created":"2023-01-16T09:52:58Z","doi":"10.1063/5.0104290","date_published":"2022-10-14T00:00:00Z","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,"publisher":"AIP Publishing","quality_controlled":"1"},{"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 2022;27:1-38. doi:10.1214/22-ejp838","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-ejp838","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.","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.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"No","external_id":{"isi":["000910863700003"]},"author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"title":"Optimal multi-resolvent local laws for Wigner matrices","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,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","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","_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_updated":"2023-08-04T10:32:23Z","ddc":["510"],"file_date_updated":"2023-01-30T11:59:21Z","department":[{"_id":"LaEr"}],"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","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},{"file":[{"file_name":"2022_JourStatisticalPhysics_Henheik.pdf","date_created":"2022-08-08T07:36:34Z","file_size":419563,"date_updated":"2022-08-08T07:36:34Z","creator":"dernst","success":1,"checksum":"b398c4dbf65f71d417981d6e366427e9","file_id":"11746","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["0022-4715"],"eissn":["1572-9613"]},"publication_status":"published","volume":189,"ec_funded":1,"oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"month":"07","intvolume":" 189","scopus_import":"1","ddc":["530"],"date_updated":"2023-09-05T14:57:49Z","file_date_updated":"2022-08-08T07:36:34Z","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"_id":"11732","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)"},"day":"29","publication":"Journal of Statistical Physics","isi":1,"has_accepted_license":"1","year":"2022","doi":"10.1007/s10955-022-02965-9","date_published":"2022-07-29T00:00:00Z","date_created":"2022-08-05T11:36:56Z","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)","quality_controlled":"1","publisher":"Springer Nature","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"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.","ieee":"S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal of Statistical Physics, vol. 189. Springer Nature, 2022.","short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (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","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."},"title":"The BCS energy gap at high density","author":[{"first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","last_name":"Henheik"},{"first_name":"Asbjørn Bækgaard","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","full_name":"Lauritsen, Asbjørn Bækgaard","orcid":"0000-0003-4476-2288","last_name":"Lauritsen"}],"external_id":{"isi":["000833007200002"]},"article_processing_charge":"Yes (via OA deal)","article_number":"5","project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}]},{"publication":"Electronic Journal of Probability","day":"28","year":"2021","has_accepted_license":"1","date_created":"2021-11-14T23:01:25Z","date_published":"2021-09-28T00:00:00Z","doi":"10.1214/21-EJP686","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.","oa":1,"publisher":"Institute of Mathematical Statistics","quality_controlled":"1","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"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.","ama":"Dubach G. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP686","apa":"Dubach, G. (2021). On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP686","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.","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.","ista":"Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 26, 124."},"title":"On eigenvector statistics in the spherical and truncated unitary ensembles","article_processing_charge":"No","author":[{"full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach","first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"}],"article_number":"124","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"language":[{"iso":"eng"}],"file":[{"relation":"main_file","access_level":"open_access","content_type":"application/pdf","success":1,"file_id":"10288","checksum":"1c975afb31460277ce4d22b93538e5f9","creator":"cchlebak","file_size":735940,"date_updated":"2021-11-15T10:10:17Z","file_name":"2021_ElecJournalProb_Dubach.pdf","date_created":"2021-11-15T10:10:17Z"}],"publication_status":"published","publication_identifier":{"eissn":["1083-6489"]},"ec_funded":1,"volume":26,"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."}],"intvolume":" 26","month":"09","scopus_import":"1","ddc":["519"],"date_updated":"2021-11-15T10:48:46Z","file_date_updated":"2021-11-15T10:10:17Z","department":[{"_id":"LaEr"}],"_id":"10285","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"},{"article_number":"2103.04817","_id":"9230","status":"public","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"type":"preprint","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.","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. .","short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).","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","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"},"date_updated":"2023-05-03T10:22:59Z","title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","department":[{"_id":"LaEr"}],"author":[{"first_name":"Louis-Pierre","last_name":"Arguin","full_name":"Arguin, Louis-Pierre"},{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","first_name":"Guillaume","orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","last_name":"Dubach"},{"full_name":"Hartung, Lisa","last_name":"Hartung","first_name":"Lisa"}],"article_processing_charge":"No","external_id":{"arxiv":["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"}],"month":"03","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.04817"}],"oa":1,"day":"08","language":[{"iso":"eng"}],"publication":"arXiv","publication_status":"submitted","year":"2021","doi":"10.48550/arXiv.2103.04817","date_published":"2021-03-08T00:00:00Z","ec_funded":1,"date_created":"2021-03-09T11:08:15Z"},{"date_updated":"2023-05-03T10:26:45Z","citation":{"mla":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” ArXiv, 2103.11389, 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. .","ama":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv. doi:10.48550/arXiv.2103.11389","apa":"Dubach, G., & Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence proof. arXiv. https://doi.org/10.48550/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.","ista":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv, 2103.11389."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2103.11389"]},"article_processing_charge":"No","author":[{"orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","last_name":"Dubach","first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"},{"last_name":"Mühlböck","full_name":"Mühlböck, Fabian","orcid":"0000-0003-1548-0177","id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425","first_name":"Fabian"}],"department":[{"_id":"LaEr"},{"_id":"ToHe"}],"title":"Formal verification of Zagier's one-sentence proof","_id":"9281","article_number":"2103.11389","type":"preprint","status":"public","project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"year":"2021","publication_status":"submitted","language":[{"iso":"eng"}],"publication":"arXiv","day":"21","date_created":"2021-03-23T05:38:48Z","ec_funded":1,"related_material":{"record":[{"relation":"other","id":"9946","status":"public"}]},"doi":"10.48550/arXiv.2103.11389","date_published":"2021-03-21T00:00:00Z","abstract":[{"lang":"eng","text":"We comment on two formal proofs of Fermat's sum of two squares theorem, written using the Mathematical Components libraries of the Coq proof assistant. The first one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's recent new proof relying on partition-theoretic arguments. Both formal proofs rely on a general property of involutions of finite sets, of independent interest. The proof technique consists for the most part of automating recurrent tasks (such as case distinctions and computations on natural numbers) via ad hoc tactics."}],"oa_version":"Preprint","oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/2103.11389","open_access":"1"}],"month":"03"},{"publication_status":"published","publication_identifier":{"issn":["0024-3795"]},"language":[{"iso":"eng"}],"ec_funded":1,"volume":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","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.11678"}],"intvolume":" 609","month":"01","date_updated":"2023-08-04T10:58:14Z","department":[{"_id":"LaEr"}],"_id":"8373","type":"journal_article","article_type":"original","keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"status":"public","year":"2021","isi":1,"publication":"Linear Algebra and its Applications","day":"15","page":"203-217","date_created":"2020-09-11T08:35:50Z","date_published":"2021-01-15T00:00:00Z","doi":"10.1016/j.laa.2020.09.007","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.","oa":1,"quality_controlled":"1","publisher":"Elsevier","citation":{"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.","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.","short":"J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.","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","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.","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."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","external_id":{"arxiv":["2002.11678"],"isi":["000581730500011"]},"article_processing_charge":"No","author":[{"first_name":"József","full_name":"Pitrik, József","last_name":"Pitrik"},{"orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","last_name":"Virosztek","first_name":"Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","project":[{"grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"},{"name":"International IST Postdoc Fellowship Programme","grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}]}]