[{"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","type":"journal_article","month":"07","_id":"11332","oa_version":"Published Version","date_updated":"2025-06-11T14:01:05Z","date_created":"2022-04-24T22:01:44Z","quality_controlled":"1","volume":393,"scopus_import":"1","project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"doi":"10.1007/s00220-022-04377-y","file_date_updated":"2022-08-05T06:01:13Z","license":"https://creativecommons.org/licenses/by/4.0/","department":[{"_id":"LaEr"}],"publisher":"Springer Nature","citation":{"chicago":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00220-022-04377-y\">https://doi.org/10.1007/s00220-022-04377-y</a>.","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907.","mla":"Schnelli, Kevin, and Yuanyuan Xu. “Convergence Rate to the Tracy–Widom Laws for the Largest Eigenvalue of Wigner Matrices.” <i>Communications in Mathematical Physics</i>, vol. 393, Springer Nature, 2022, pp. 839–907, doi:<a href=\"https://doi.org/10.1007/s00220-022-04377-y\">10.1007/s00220-022-04377-y</a>.","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.","ieee":"K. Schnelli and Y. Xu, “Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices,” <i>Communications in Mathematical Physics</i>, vol. 393. Springer Nature, pp. 839–907, 2022.","apa":"Schnelli, K., &#38; Xu, Y. (2022). Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-022-04377-y\">https://doi.org/10.1007/s00220-022-04377-y</a>","ama":"Schnelli K, Xu Y. Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices. <i>Communications in Mathematical Physics</i>. 2022;393:839-907. doi:<a href=\"https://doi.org/10.1007/s00220-022-04377-y\">10.1007/s00220-022-04377-y</a>"},"date_published":"2022-07-01T00:00:00Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"       393","status":"public","ec_funded":1,"arxiv":1,"oa":1,"article_processing_charge":"No","author":[{"orcid":"0000-0003-0954-3231","last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","first_name":"Kevin","full_name":"Schnelli, Kevin"},{"orcid":"0000-0003-1559-1205","last_name":"Xu","id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","full_name":"Xu, Yuanyuan","first_name":"Yuanyuan"}],"day":"01","ddc":["510"],"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."}],"title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","publication_status":"published","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.","publication":"Communications in Mathematical Physics","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"file":[{"creator":"dernst","success":1,"file_size":1141462,"date_created":"2022-08-05T06:01:13Z","date_updated":"2022-08-05T06:01:13Z","access_level":"open_access","content_type":"application/pdf","file_name":"2022_CommunMathPhys_Schnelli.pdf","relation":"main_file","file_id":"11726","checksum":"bee0278c5efa9a33d9a2dc8d354a6c51"}],"isi":1,"pmid":1,"external_id":{"isi":["000782737200001"],"arxiv":["2102.04330"],"pmid":["35765414"]},"language":[{"iso":"eng"}],"year":"2022","article_type":"original"},{"arxiv":1,"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"        50","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. 2022;50(3):984-1012. doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Normal fluctuation in quantum ergodicity for Wigner matrices. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Normal fluctuation in quantum ergodicity for Wigner matrices,” <i>Annals of Probability</i>, vol. 50, no. 3. Institute of Mathematical Statistics, pp. 984–1012, 2022.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Normal fluctuation in quantum ergodicity for Wigner matrices. Annals of Probability. 50(3), 984–1012.","mla":"Cipolloni, Giorgio, et al. “Normal Fluctuation in Quantum Ergodicity for Wigner Matrices.” <i>Annals of Probability</i>, vol. 50, no. 3, Institute of Mathematical Statistics, 2022, pp. 984–1012, doi:<a href=\"https://doi.org/10.1214/21-AOP1552\">10.1214/21-AOP1552</a>.","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.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/21-AOP1552\">https://doi.org/10.1214/21-AOP1552</a>."},"date_published":"2022-05-01T00:00:00Z","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"doi":"10.1214/21-AOP1552","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.06730"}],"scopus_import":"1","month":"05","_id":"11418","oa_version":"Preprint","volume":50,"date_created":"2022-05-29T22:01:53Z","date_updated":"2023-08-03T07:16:53Z","quality_controlled":"1","type":"journal_article","year":"2022","article_type":"original","external_id":{"arxiv":["2103.06730"],"isi":["000793963400005"]},"language":[{"iso":"eng"}],"isi":1,"publication_identifier":{"issn":["0091-1798"],"eissn":["2168-894X"]},"publication":"Annals of Probability","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.","publication_status":"published","page":"984-1012","title":"Normal fluctuation in quantum ergodicity for Wigner matrices","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"}],"author":[{"first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder"}],"day":"01","issue":"3","article_processing_charge":"No","oa":1},{"publisher":"Springer Nature","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"file_date_updated":"2022-08-08T07:36:34Z","ec_funded":1,"corr_author":"1","status":"public","article_number":"5","date_published":"2022-07-29T00:00:00Z","citation":{"ama":"Henheik SJ, Lauritsen AB. The BCS energy gap at high density. <i>Journal of Statistical Physics</i>. 2022;189. doi:<a href=\"https://doi.org/10.1007/s10955-022-02965-9\">10.1007/s10955-022-02965-9</a>","ieee":"S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” <i>Journal of Statistical Physics</i>, vol. 189. Springer Nature, 2022.","apa":"Henheik, S. J., &#38; Lauritsen, A. B. (2022). The BCS energy gap at high density. <i>Journal of Statistical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s10955-022-02965-9\">https://doi.org/10.1007/s10955-022-02965-9</a>","ista":"Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5.","short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” <i>Journal of Statistical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s10955-022-02965-9\">https://doi.org/10.1007/s10955-022-02965-9</a>.","mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” <i>Journal of Statistical Physics</i>, vol. 189, 5, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s10955-022-02965-9\">10.1007/s10955-022-02965-9</a>."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","intvolume":"       189","related_material":{"record":[{"id":"19540","relation":"dissertation_contains","status":"public"},{"relation":"dissertation_contains","id":"18135","status":"public"}]},"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","type":"journal_article","doi":"10.1007/s10955-022-02965-9","date_created":"2022-08-05T11:36:56Z","volume":189,"quality_controlled":"1","date_updated":"2026-04-07T13:01:40Z","_id":"11732","oa_version":"Published Version","month":"07","project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"scopus_import":"1","publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"isi":1,"file":[{"content_type":"application/pdf","access_level":"open_access","success":1,"creator":"dernst","date_updated":"2022-08-08T07:36:34Z","date_created":"2022-08-08T07:36:34Z","file_size":419563,"checksum":"b398c4dbf65f71d417981d6e366427e9","file_name":"2022_JourStatisticalPhysics_Henheik.pdf","file_id":"11746","relation":"main_file"}],"publication":"Journal of Statistical Physics","article_type":"original","year":"2022","language":[{"iso":"eng"}],"external_id":{"isi":["000833007200002"]},"ddc":["530"],"day":"29","author":[{"last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha"},{"orcid":"0000-0003-4476-2288","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","last_name":"Lauritsen","first_name":"Asbjørn Bækgaard","full_name":"Lauritsen, Asbjørn Bækgaard"}],"oa":1,"article_processing_charge":"Yes (via OA deal)","publication_status":"published","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)","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."}],"title":"The BCS energy gap at high density"},{"year":"2022","article_type":"original","external_id":{"isi":["000900748900002"]},"language":[{"iso":"eng"}],"file":[{"file_name":"2022_JourMathPhysics_Henheik.pdf","relation":"main_file","file_id":"12327","checksum":"5150287295e0ce4f12462c990744d65d","creator":"dernst","success":1,"date_created":"2023-01-20T11:58:59Z","date_updated":"2023-01-20T11:58:59Z","file_size":5436804,"access_level":"open_access","content_type":"application/pdf"}],"isi":1,"publication_identifier":{"issn":["0022-2488"]},"publication":"Journal of Mathematical Physics","acknowledgement":"J.H. gratefully acknowledges the partial financial support by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331.\r\n","publication_status":"published","title":"Interior-boundary conditions for the Dirac equation at point sources in three dimensions","abstract":[{"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.","lang":"eng"}],"author":[{"orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha"},{"last_name":"Tumulka","first_name":"Roderich","full_name":"Tumulka, Roderich"}],"day":"01","ddc":["510"],"issue":"12","article_processing_charge":"No","oa":1,"article_number":"122302","status":"public","corr_author":"1","ec_funded":1,"intvolume":"        63","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"chicago":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0104675\">https://doi.org/10.1063/5.0104675</a>.","short":"S.J. Henheik, R. Tumulka, Journal of Mathematical Physics 63 (2022).","mla":"Henheik, Sven Joscha, and Roderich Tumulka. “Interior-Boundary Conditions for the Dirac Equation at Point Sources in Three Dimensions.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12, 122302, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0104675\">10.1063/5.0104675</a>.","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.","ieee":"S. J. Henheik and R. Tumulka, “Interior-boundary conditions for the Dirac equation at point sources in three dimensions,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12. AIP Publishing, 2022.","apa":"Henheik, S. J., &#38; Tumulka, R. (2022). Interior-boundary conditions for the Dirac equation at point sources in three dimensions. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0104675\">https://doi.org/10.1063/5.0104675</a>","ama":"Henheik SJ, Tumulka R. Interior-boundary conditions for the Dirac equation at point sources in three dimensions. <i>Journal of Mathematical Physics</i>. 2022;63(12). doi:<a href=\"https://doi.org/10.1063/5.0104675\">10.1063/5.0104675</a>"},"date_published":"2022-12-01T00:00:00Z","publisher":"AIP Publishing","file_date_updated":"2023-01-20T11:58:59Z","department":[{"_id":"LaEr"}],"doi":"10.1063/5.0104675","scopus_import":"1","project":[{"grant_number":"101020331","call_identifier":"H2020","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"month":"12","_id":"12110","oa_version":"Published Version","date_updated":"2025-04-14T07:57:18Z","quality_controlled":"1","volume":63,"date_created":"2023-01-08T23:00:53Z","type":"journal_article","has_accepted_license":"1","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}},{"article_type":"original","year":"2022","language":[{"iso":"eng"}],"external_id":{"isi":["000873719200001"]},"publication_identifier":{"issn":["2050-5094"]},"isi":1,"file":[{"creator":"dernst","success":1,"date_created":"2023-01-24T10:02:40Z","file_size":817089,"date_updated":"2023-01-24T10:02:40Z","content_type":"application/pdf","access_level":"open_access","file_name":"2022_ForumMath_Cipolloni.pdf","file_id":"12356","relation":"main_file","checksum":"94a049aeb1eea5497aa097712a73c400"}],"publication":"Forum of Mathematics, Sigma","publication_status":"published","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.","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."}],"title":"Rank-uniform local law for Wigner matrices","day":"27","ddc":["510"],"author":[{"full_name":"Cipolloni, Giorgio","first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","first_name":"László"},{"orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"oa":1,"article_processing_charge":"No","ec_funded":1,"status":"public","corr_author":"1","article_number":"e96","date_published":"2022-10-27T00:00:00Z","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Rank-uniform local law for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Rank-uniform local law for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","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.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e96, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2022.86\">10.1017/fms.2022.86</a>.","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.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2022.86\">https://doi.org/10.1017/fms.2022.86</a>."},"intvolume":"        10","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Cambridge University Press","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-24T10:02:40Z","doi":"10.1017/fms.2022.86","date_updated":"2025-04-14T07:57:18Z","volume":10,"date_created":"2023-01-12T12:07:30Z","quality_controlled":"1","_id":"12148","oa_version":"Published Version","month":"10","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020"}],"scopus_import":"1","keyword":["Computational Mathematics","Discrete Mathematics and Combinatorics","Geometry and Topology","Mathematical Physics","Statistics and Probability","Algebra and Number Theory","Theoretical Computer Science","Analysis"],"has_accepted_license":"1","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"type":"journal_article"},{"abstract":[{"lang":"eng","text":"We derive an accurate lower tail estimate on the lowest singular value σ1(X−z) of a real Gaussian (Ginibre) random matrix X shifted by a complex parameter z. Such shift effectively changes the upper tail behavior of the condition number κ(X−z) from the slower (κ(X−z)≥t)≲1/t decay typical for real Ginibre matrices to the faster 1/t2 decay seen for complex Ginibre matrices as long as z is away from the real axis. This sharpens and resolves a recent conjecture in [J. Banks et al., https://arxiv.org/abs/2005.08930, 2020] on the regularizing effect of the real Ginibre ensemble with a genuinely complex shift. As a consequence we obtain an improved upper bound on the eigenvalue condition numbers (known also as the eigenvector overlaps) for real Ginibre matrices. The main technical tool is a rigorous supersymmetric analysis from our earlier work [Probab. Math. Phys., 1 (2020), pp. 101--146]."}],"title":"On the condition number of the shifted real Ginibre ensemble","page":"1469-1487","publication_status":"published","oa":1,"article_processing_charge":"No","issue":"3","day":"01","author":[{"first_name":"Giorgio","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J","full_name":"Schröder, Dominik J"}],"language":[{"iso":"eng"}],"external_id":{"isi":["001125796400002"],"arxiv":["2105.13719"]},"article_type":"original","year":"2022","publication":"SIAM Journal on Matrix Analysis and Applications","publication_identifier":{"issn":["0895-4798"],"eissn":["1095-7162"]},"isi":1,"volume":43,"quality_controlled":"1","date_updated":"2025-09-10T09:51:27Z","date_created":"2023-01-12T12:12:38Z","month":"07","_id":"12179","oa_version":"Preprint","scopus_import":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2105.13719","open_access":"1"}],"doi":"10.1137/21m1424408","type":"journal_article","keyword":["Analysis"],"citation":{"apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). On the condition number of the shifted real Ginibre ensemble. <i>SIAM Journal on Matrix Analysis and Applications</i>. Society for Industrial and Applied Mathematics. <a href=\"https://doi.org/10.1137/21m1424408\">https://doi.org/10.1137/21m1424408</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the condition number of the shifted real Ginibre ensemble,” <i>SIAM Journal on Matrix Analysis and Applications</i>, vol. 43, no. 3. Society for Industrial and Applied Mathematics, pp. 1469–1487, 2022.","ama":"Cipolloni G, Erdös L, Schröder DJ. On the condition number of the shifted real Ginibre ensemble. <i>SIAM Journal on Matrix Analysis and Applications</i>. 2022;43(3):1469-1487. doi:<a href=\"https://doi.org/10.1137/21m1424408\">10.1137/21m1424408</a>","mla":"Cipolloni, Giorgio, et al. “On the Condition Number of the Shifted Real Ginibre Ensemble.” <i>SIAM Journal on Matrix Analysis and Applications</i>, vol. 43, no. 3, Society for Industrial and Applied Mathematics, 2022, pp. 1469–87, doi:<a href=\"https://doi.org/10.1137/21m1424408\">10.1137/21m1424408</a>.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Condition Number of the Shifted Real Ginibre Ensemble.” <i>SIAM Journal on Matrix Analysis and Applications</i>. Society for Industrial and Applied Mathematics, 2022. <a href=\"https://doi.org/10.1137/21m1424408\">https://doi.org/10.1137/21m1424408</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, SIAM Journal on Matrix Analysis and Applications 43 (2022) 1469–1487.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. On the condition number of the shifted real Ginibre ensemble. SIAM Journal on Matrix Analysis and Applications. 43(3), 1469–1487."},"date_published":"2022-07-01T00:00:00Z","intvolume":"        43","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","status":"public","corr_author":"1","arxiv":1,"department":[{"_id":"LaEr"}],"publisher":"Society for Industrial and Applied Mathematics"},{"article_type":"original","year":"2022","language":[{"iso":"eng"}],"external_id":{"arxiv":["2208.12220"],"isi":["000905776200001"]},"publication_identifier":{"issn":["0022-2488"]},"isi":1,"file":[{"checksum":"213b93750080460718c050e4967cfdb4","file_id":"12410","relation":"main_file","file_name":"2022_JourMathPhysics_Henheik2.pdf","content_type":"application/pdf","access_level":"open_access","file_size":5251092,"date_updated":"2023-01-27T07:10:52Z","date_created":"2023-01-27T07:10:52Z","creator":"dernst","success":1}],"publication":"Journal of Mathematical Physics","publication_status":"published","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.\" ","abstract":[{"lang":"eng","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."}],"title":"On adiabatic theory for extended fermionic lattice systems","issue":"12","ddc":["510"],"day":"01","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha"},{"last_name":"Wessel","first_name":"Tom","full_name":"Wessel, Tom"}],"oa":1,"article_processing_charge":"No","ec_funded":1,"status":"public","corr_author":"1","arxiv":1,"article_number":"121101","citation":{"ama":"Henheik SJ, Wessel T. On adiabatic theory for extended fermionic lattice systems. <i>Journal of Mathematical Physics</i>. 2022;63(12). doi:<a href=\"https://doi.org/10.1063/5.0123441\">10.1063/5.0123441</a>","ieee":"S. J. Henheik and T. Wessel, “On adiabatic theory for extended fermionic lattice systems,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12. AIP Publishing, 2022.","apa":"Henheik, S. J., &#38; Wessel, T. (2022). On adiabatic theory for extended fermionic lattice systems. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0123441\">https://doi.org/10.1063/5.0123441</a>","ista":"Henheik SJ, Wessel T. 2022. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 63(12), 121101.","short":"S.J. Henheik, T. Wessel, Journal of Mathematical Physics 63 (2022).","chicago":"Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0123441\">https://doi.org/10.1063/5.0123441</a>.","mla":"Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 12, 121101, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0123441\">10.1063/5.0123441</a>."},"date_published":"2022-12-01T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"        63","publisher":"AIP Publishing","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-27T07:10:52Z","doi":"10.1063/5.0123441","date_updated":"2026-04-07T12:37:10Z","quality_controlled":"1","volume":63,"date_created":"2023-01-15T23:00:52Z","_id":"12184","oa_version":"Published Version","month":"12","project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"scopus_import":"1","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"19540"}]},"has_accepted_license":"1","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"type":"journal_article"},{"publication_identifier":{"eissn":["1469-7750"],"issn":["0024-6107"]},"isi":1,"publication":"Journal of the London Mathematical Society","article_type":"original","year":"2022","language":[{"iso":"eng"}],"external_id":{"isi":["000854878500001"],"arxiv":["2102.02037"]},"issue":"4","day":"18","author":[{"last_name":"Gehér","full_name":"Gehér, György Pál","first_name":"György Pál"},{"last_name":"Titkos","first_name":"Tamás","full_name":"Titkos, Tamás"},{"orcid":"0000-0003-1109-5511","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","full_name":"Virosztek, Daniel","first_name":"Daniel"}],"oa":1,"article_processing_charge":"No","page":"3865-3894","publication_status":"published","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). ","abstract":[{"lang":"eng","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. "}],"title":"The isometry group of Wasserstein spaces: The Hilbertian case","publisher":"Wiley","department":[{"_id":"LaEr"}],"ec_funded":1,"status":"public","arxiv":1,"date_published":"2022-09-18T00:00:00Z","citation":{"apa":"Gehér, G. P., Titkos, T., &#38; Virosztek, D. (2022). The isometry group of Wasserstein spaces: The Hilbertian case. <i>Journal of the London Mathematical Society</i>. Wiley. <a href=\"https://doi.org/10.1112/jlms.12676\">https://doi.org/10.1112/jlms.12676</a>","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “The isometry group of Wasserstein spaces: The Hilbertian case,” <i>Journal of the London Mathematical Society</i>, 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. <i>Journal of the London Mathematical Society</i>. 2022;106(4):3865-3894. doi:<a href=\"https://doi.org/10.1112/jlms.12676\">10.1112/jlms.12676</a>","mla":"Gehér, György Pál, et al. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” <i>Journal of the London Mathematical Society</i>, vol. 106, no. 4, Wiley, 2022, pp. 3865–94, doi:<a href=\"https://doi.org/10.1112/jlms.12676\">10.1112/jlms.12676</a>.","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.” <i>Journal of the London Mathematical Society</i>. Wiley, 2022. <a href=\"https://doi.org/10.1112/jlms.12676\">https://doi.org/10.1112/jlms.12676</a>.","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","intvolume":"       106","keyword":["General Mathematics"],"type":"journal_article","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2102.02037"}],"doi":"10.1112/jlms.12676","volume":106,"quality_controlled":"1","date_created":"2023-01-16T09:46:13Z","date_updated":"2025-04-14T07:50:40Z","_id":"12214","oa_version":"Preprint","month":"09","project":[{"name":"Geometric study of Wasserstein spaces and free probability","_id":"26A455A6-B435-11E9-9278-68D0E5697425","grant_number":"846294","call_identifier":"H2020"}],"scopus_import":"1"},{"page":"3981-4002","publication_status":"published","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.","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"}],"title":"Density of small singular values of the shifted real Ginibre ensemble","issue":"11","day":"01","ddc":["510"],"author":[{"orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J"}],"oa":1,"article_processing_charge":"No","article_type":"original","year":"2022","language":[{"iso":"eng"}],"external_id":{"isi":["000796323500001"]},"publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"isi":1,"file":[{"file_name":"2022_AnnalesHenriP_Cipolloni.pdf","relation":"main_file","file_id":"12424","checksum":"5582f059feeb2f63e2eb68197a34d7dc","creator":"dernst","success":1,"date_created":"2023-01-27T11:06:47Z","file_size":1333638,"date_updated":"2023-01-27T11:06:47Z","access_level":"open_access","content_type":"application/pdf"}],"publication":"Annales Henri Poincaré","doi":"10.1007/s00023-022-01188-8","date_updated":"2023-08-04T09:33:52Z","volume":23,"quality_controlled":"1","date_created":"2023-01-16T09:50:26Z","_id":"12232","oa_version":"Published Version","month":"11","scopus_import":"1","keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"has_accepted_license":"1","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"type":"journal_article","status":"public","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.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>.","mla":"Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” <i>Annales Henri Poincaré</i>, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>.","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. 2022;23(11):3981-4002. doi:<a href=\"https://doi.org/10.1007/s00023-022-01188-8\">10.1007/s00023-022-01188-8</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” <i>Annales Henri Poincaré</i>, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. <i>Annales Henri Poincaré</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-022-01188-8\">https://doi.org/10.1007/s00023-022-01188-8</a>"},"date_published":"2022-11-01T00:00:00Z","intvolume":"        23","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publisher":"Springer Nature","department":[{"_id":"LaEr"}],"file_date_updated":"2023-01-27T11:06:47Z"},{"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"type":"journal_article","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","doi":"10.1063/5.0104290","scopus_import":"1","project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"_id":"12243","oa_version":"Published Version","month":"10","quality_controlled":"1","date_created":"2023-01-16T09:52:58Z","volume":63,"date_updated":"2025-04-14T07:57:18Z","publisher":"AIP Publishing","file_date_updated":"2023-01-30T08:01:10Z","department":[{"_id":"LaEr"}],"arxiv":1,"article_number":"103303","status":"public","ec_funded":1,"intvolume":"        63","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2022-10-14T00:00:00Z","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for Ginibre eigenvalues. <i>Journal of Mathematical Physics</i>. 2022;63(10). doi:<a href=\"https://doi.org/10.1063/5.0104290\">10.1063/5.0104290</a>","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., &#38; Xu, Y. (2022). Directional extremal statistics for Ginibre eigenvalues. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0104290\">https://doi.org/10.1063/5.0104290</a>","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 10. AIP Publishing, 2022.","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303.","mla":"Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 10, 103303, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0104290\">10.1063/5.0104290</a>.","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “Directional Extremal Statistics for Ginibre Eigenvalues.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0104290\">https://doi.org/10.1063/5.0104290</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022)."},"author":[{"full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992"},{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","last_name":"Xu","orcid":"0000-0003-1559-1205","full_name":"Xu, Yuanyuan","first_name":"Yuanyuan"}],"ddc":["510","530"],"day":"14","issue":"10","article_processing_charge":"Yes (via OA deal)","oa":1,"acknowledgement":"The authors are grateful to G. Akemann for bringing Refs. 19 and 24–26 to their attention. Discussions with Guillaume Dubach on a preliminary version of this project are acknowledged.\r\nL.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331. D.S. was supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","publication_status":"published","title":"Directional extremal statistics for Ginibre eigenvalues","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)]. "}],"file":[{"access_level":"open_access","content_type":"application/pdf","date_created":"2023-01-30T08:01:10Z","date_updated":"2023-01-30T08:01:10Z","file_size":7356807,"creator":"dernst","success":1,"checksum":"2db278ae5b07f345a7e3fec1f92b5c33","relation":"main_file","file_id":"12436","file_name":"2022_JourMathPhysics_Cipolloni2.pdf"}],"isi":1,"publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"publication":"Journal of Mathematical Physics","year":"2022","article_type":"original","external_id":{"isi":["000869715800001"],"arxiv":["2206.04443"]},"language":[{"iso":"eng"}]},{"publication":"Electronic Journal of Probability","publication_identifier":{"eissn":["1083-6489"]},"file":[{"checksum":"bb647b48fbdb59361210e425c220cdcb","file_name":"2022_ElecJournProbability_Cipolloni.pdf","file_id":"12464","relation":"main_file","content_type":"application/pdf","access_level":"open_access","success":1,"creator":"dernst","date_updated":"2023-01-30T11:59:21Z","date_created":"2023-01-30T11:59:21Z","file_size":502149}],"isi":1,"external_id":{"isi":["000910863700003"]},"language":[{"iso":"eng"}],"year":"2022","article_type":"original","oa":1,"article_processing_charge":"No","author":[{"first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni"},{"last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","full_name":"Schröder, Dominik J","first_name":"Dominik J"}],"ddc":["510"],"day":"12","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"}],"title":"Optimal multi-resolvent local laws for Wigner matrices","publication_status":"published","page":"1-38","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.","file_date_updated":"2023-01-30T11:59:21Z","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","date_published":"2022-09-12T00:00:00Z","citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” <i>Electronic Journal of Probability</i>, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. <i>Electronic Journal of Probability</i>. 2022;27:1-38. doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2022. <a href=\"https://doi.org/10.1214/22-ejp838\">https://doi.org/10.1214/22-ejp838</a>.","mla":"Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” <i>Electronic Journal of Probability</i>, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:<a href=\"https://doi.org/10.1214/22-ejp838\">10.1214/22-ejp838</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38."},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"        27","corr_author":"1","status":"public","ec_funded":1,"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","type":"journal_article","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"_id":"12290","month":"09","oa_version":"Published Version","date_updated":"2025-04-14T07:57:19Z","date_created":"2023-01-16T10:04:38Z","quality_controlled":"1","volume":27,"scopus_import":"1","project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"doi":"10.1214/22-ejp838"},{"article_processing_charge":"No","oa":1,"day":"03","author":[{"last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha"},{"first_name":"Stefan","full_name":"Teufel, Stefan","last_name":"Teufel"}],"issue":"1","title":"Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap","abstract":[{"text":"We show that recent results on adiabatic theory for interacting gapped many-body systems on finite lattices remain valid in the thermodynamic limit. More precisely, we prove a generalized super-adiabatic theorem for the automorphism group describing the infinite volume dynamics on the quasi-local algebra of observables. The key assumption is the existence of a sequence of gapped finite volume Hamiltonians, which generates the same infinite volume dynamics in the thermodynamic limit. Our adiabatic theorem also holds for certain perturbations of gapped ground states that close the spectral gap (so it is also an adiabatic theorem for resonances and, in this sense, “generalized”), and it provides an adiabatic approximation to all orders in the adiabatic parameter (a property often called “super-adiabatic”). In addition to the existing results for finite lattices, we also perform a resummation of the adiabatic expansion and allow for observables that are not strictly local. Finally, as an application, we prove the validity of linear and higher order response theory for our class of perturbations for infinite systems. While we consider the result and its proof as new and interesting in itself, we also lay the foundation for the proof of an adiabatic theorem for systems with a gap only in the bulk, which will be presented in a follow-up article.","lang":"eng"}],"acknowledgement":"J.H. acknowledges partial financial support from ERC Advanced Grant “RMTBeyond” No. 101020331.","publication_status":"published","publication":"Journal of Mathematical Physics","isi":1,"publication_identifier":{"eissn":["1089-7658"],"issn":["0022-2488"]},"language":[{"iso":"eng"}],"external_id":{"arxiv":["2012.15238"],"isi":["000739446000009"]},"article_type":"original","year":"2022","type":"journal_article","keyword":["mathematical physics","statistical and nonlinear physics"],"project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"scopus_import":"1","date_created":"2022-01-03T12:19:48Z","volume":63,"quality_controlled":"1","date_updated":"2025-04-14T07:57:17Z","oa_version":"Preprint","_id":"10600","month":"01","doi":"10.1063/5.0051632","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2012.15238","open_access":"1"}],"department":[{"_id":"GradSch"},{"_id":"LaEr"}],"publisher":"AIP Publishing","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"        63","citation":{"ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap,” <i>Journal of Mathematical Physics</i>, vol. 63, no. 1. AIP Publishing, 2022.","apa":"Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. <i>Journal of Mathematical Physics</i>. AIP Publishing. <a href=\"https://doi.org/10.1063/5.0051632\">https://doi.org/10.1063/5.0051632</a>","ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. <i>Journal of Mathematical Physics</i>. 2022;63(1). doi:<a href=\"https://doi.org/10.1063/5.0051632\">10.1063/5.0051632</a>","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Uniform Gap.” <i>Journal of Mathematical Physics</i>. AIP Publishing, 2022. <a href=\"https://doi.org/10.1063/5.0051632\">https://doi.org/10.1063/5.0051632</a>.","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.” <i>Journal of Mathematical Physics</i>, vol. 63, no. 1, 011901, AIP Publishing, 2022, doi:<a href=\"https://doi.org/10.1063/5.0051632\">10.1063/5.0051632</a>.","ista":"Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a uniform gap. Journal of Mathematical Physics. 63(1), 011901."},"date_published":"2022-01-03T00:00:00Z","article_number":"011901","arxiv":1,"ec_funded":1,"status":"public"},{"isi":1,"file":[{"creator":"cchlebak","success":1,"file_size":505804,"date_created":"2022-01-14T07:27:45Z","date_updated":"2022-01-14T07:27:45Z","content_type":"application/pdf","access_level":"open_access","file_name":"2022_MathPhyAnalGeo_Henheik.pdf","file_id":"10624","relation":"main_file","checksum":"d44f8123a52592a75b2c3b8ee2cd2435"}],"publication_identifier":{"issn":["1385-0172"],"eissn":["1572-9656"]},"publication":"Mathematical Physics, Analysis and Geometry","article_type":"original","year":"2022","language":[{"iso":"eng"}],"external_id":{"arxiv":["2106.02015"],"isi":["000741387600001"]},"ddc":["514"],"day":"11","author":[{"full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","orcid":"0000-0003-1106-327X","last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"}],"issue":"1","article_processing_charge":"Yes (via OA deal)","oa":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.","publication_status":"published","title":"The BCS critical temperature at high density","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"}],"publisher":"Springer Nature","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-14T07:27:45Z","article_number":"3","arxiv":1,"ec_funded":1,"corr_author":"1","status":"public","intvolume":"        25","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","date_published":"2022-01-11T00:00:00Z","citation":{"ista":"Henheik SJ. 2022. The BCS critical temperature at high density. Mathematical Physics, Analysis and Geometry. 25(1), 3.","short":"S.J. Henheik, Mathematical Physics, Analysis and Geometry 25 (2022).","chicago":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s11040-021-09415-0\">https://doi.org/10.1007/s11040-021-09415-0</a>.","mla":"Henheik, Sven Joscha. “The BCS Critical Temperature at High Density.” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 25, no. 1, 3, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s11040-021-09415-0\">10.1007/s11040-021-09415-0</a>.","ama":"Henheik SJ. The BCS critical temperature at high density. <i>Mathematical Physics, Analysis and Geometry</i>. 2022;25(1). doi:<a href=\"https://doi.org/10.1007/s11040-021-09415-0\">10.1007/s11040-021-09415-0</a>","ieee":"S. J. Henheik, “The BCS critical temperature at high density,” <i>Mathematical Physics, Analysis and Geometry</i>, vol. 25, no. 1. Springer Nature, 2022.","apa":"Henheik, S. J. (2022). The BCS critical temperature at high density. <i>Mathematical Physics, Analysis and Geometry</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11040-021-09415-0\">https://doi.org/10.1007/s11040-021-09415-0</a>"},"related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"keyword":["geometry and topology","mathematical physics"],"type":"journal_article","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","doi":"10.1007/s11040-021-09415-0","project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"scopus_import":"1","date_created":"2022-01-13T15:40:53Z","quality_controlled":"1","volume":25,"date_updated":"2026-04-07T12:37:10Z","_id":"10623","month":"01","oa_version":"Published Version"},{"date_published":"2022-01-18T00:00:00Z","citation":{"apa":"Henheik, S. J., Teufel, S., &#38; Wessel, T. (2022). Local stability of ground states in locally gapped and weakly interacting quantum spin systems. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-021-01494-y\">https://doi.org/10.1007/s11005-021-01494-y</a>","ieee":"S. J. Henheik, S. Teufel, and T. Wessel, “Local stability of ground states in locally gapped and weakly interacting quantum spin systems,” <i>Letters in Mathematical Physics</i>, vol. 112, no. 1. Springer Nature, 2022.","ama":"Henheik SJ, Teufel S, Wessel T. Local stability of ground states in locally gapped and weakly interacting quantum spin systems. <i>Letters in Mathematical Physics</i>. 2022;112(1). doi:<a href=\"https://doi.org/10.1007/s11005-021-01494-y\">10.1007/s11005-021-01494-y</a>","mla":"Henheik, Sven Joscha, et al. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” <i>Letters in Mathematical Physics</i>, vol. 112, no. 1, 9, Springer Nature, 2022, doi:<a href=\"https://doi.org/10.1007/s11005-021-01494-y\">10.1007/s11005-021-01494-y</a>.","short":"S.J. Henheik, S. Teufel, T. Wessel, Letters in Mathematical Physics 112 (2022).","chicago":"Henheik, Sven Joscha, Stefan Teufel, and Tom Wessel. “Local Stability of Ground States in Locally Gapped and Weakly Interacting Quantum Spin Systems.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s11005-021-01494-y\">https://doi.org/10.1007/s11005-021-01494-y</a>.","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."},"intvolume":"       112","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","ec_funded":1,"status":"public","arxiv":1,"article_number":"9","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"file_date_updated":"2022-01-19T09:41:14Z","publisher":"Springer Nature","volume":112,"quality_controlled":"1","date_created":"2022-01-18T16:18:25Z","date_updated":"2026-04-07T12:37:10Z","month":"01","_id":"10642","oa_version":"Published Version","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","call_identifier":"H2020"}],"scopus_import":"1","doi":"10.1007/s11005-021-01494-y","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","type":"journal_article","related_material":{"record":[{"relation":"dissertation_contains","id":"19540","status":"public"}]},"keyword":["mathematical physics","statistical and nonlinear physics"],"language":[{"iso":"eng"}],"external_id":{"arxiv":["2106.13780"],"isi":["000744930400001"],"pmid":["35125630"]},"pmid":1,"article_type":"original","year":"2022","publication":"Letters in Mathematical Physics","publication_identifier":{"eissn":["1573-0530"],"issn":["0377-9017"]},"isi":1,"file":[{"checksum":"7e8e69b76e892c305071a4736131fe18","file_id":"10647","relation":"main_file","file_name":"2022_LettersMathPhys_Henheik.pdf","content_type":"application/pdf","access_level":"open_access","date_created":"2022-01-19T09:41:14Z","date_updated":"2022-01-19T09:41:14Z","file_size":357547,"creator":"cchlebak","success":1}],"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."}],"title":"Local stability of ground states in locally gapped and weakly interacting quantum spin systems","publication_status":"published","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.","oa":1,"article_processing_charge":"No","issue":"1","ddc":["530"],"day":"18","author":[{"last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha"},{"first_name":"Stefan","full_name":"Teufel, Stefan","last_name":"Teufel"},{"first_name":"Tom","full_name":"Wessel, Tom","last_name":"Wessel"}]},{"citation":{"ama":"Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. 2022;10. doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>","ieee":"S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,” <i>Forum of Mathematics, Sigma</i>, vol. 10. Cambridge University Press, 2022.","apa":"Henheik, S. J., &#38; Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>","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.","short":"S.J. Henheik, S. Teufel, Forum of Mathematics, Sigma 10 (2022).","chicago":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2022. <a href=\"https://doi.org/10.1017/fms.2021.80\">https://doi.org/10.1017/fms.2021.80</a>.","mla":"Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.” <i>Forum of Mathematics, Sigma</i>, vol. 10, e4, Cambridge University Press, 2022, doi:<a href=\"https://doi.org/10.1017/fms.2021.80\">10.1017/fms.2021.80</a>."},"date_published":"2022-01-18T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"        10","status":"public","corr_author":"1","ec_funded":1,"article_number":"e4","arxiv":1,"file_date_updated":"2022-01-19T09:27:43Z","department":[{"_id":"GradSch"},{"_id":"LaEr"}],"publisher":"Cambridge University Press","_id":"10643","month":"01","oa_version":"Published Version","quality_controlled":"1","date_updated":"2025-04-14T07:57:17Z","volume":10,"date_created":"2022-01-18T16:18:51Z","scopus_import":"1","project":[{"call_identifier":"H2020","grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"doi":"10.1017/fms.2021.80","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","type":"journal_article","keyword":["computational mathematics","discrete mathematics and combinatorics","geometry and topology","mathematical physics","statistics and probability","algebra and number theory","theoretical computer science","analysis"],"external_id":{"isi":["000743615000001"],"arxiv":["2012.15239"]},"language":[{"iso":"eng"}],"year":"2022","article_type":"original","publication":"Forum of Mathematics, Sigma","publication_identifier":{"eissn":["2050-5094"]},"file":[{"relation":"main_file","file_id":"10646","file_name":"2022_ForumMathSigma_Henheik.pdf","checksum":"87592a755adcef22ea590a99dc728dd3","date_updated":"2022-01-19T09:27:43Z","date_created":"2022-01-19T09:27:43Z","file_size":705323,"creator":"cchlebak","success":1,"access_level":"open_access","content_type":"application/pdf"}],"isi":1,"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"}],"title":"Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk","publication_status":"published","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.","oa":1,"article_processing_charge":"Yes","author":[{"id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha"},{"full_name":"Teufel, Stefan","first_name":"Stefan","last_name":"Teufel"}],"ddc":["510"],"day":"18"},{"tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","type":"journal_article","doi":"10.1016/j.jfa.2022.109394","_id":"10732","oa_version":"Published Version","month":"04","volume":282,"date_created":"2022-02-06T23:01:30Z","quality_controlled":"1","date_updated":"2024-10-09T21:01:33Z","scopus_import":"1","publisher":"Elsevier","file_date_updated":"2022-07-29T07:22:08Z","department":[{"_id":"LaEr"}],"corr_author":"1","status":"public","arxiv":1,"article_number":"109394","citation":{"mla":"Cipolloni, Giorgio, et al. “Thermalisation for Wigner Matrices.” <i>Journal of Functional Analysis</i>, vol. 282, no. 8, 109394, Elsevier, 2022, doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">10.1016/j.jfa.2022.109394</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Journal of Functional Analysis 282 (2022).","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Thermalisation for Wigner Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2022. <a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">https://doi.org/10.1016/j.jfa.2022.109394</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Thermalisation for Wigner matrices. Journal of Functional Analysis. 282(8), 109394.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2022). Thermalisation for Wigner matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">https://doi.org/10.1016/j.jfa.2022.109394</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Thermalisation for Wigner matrices,” <i>Journal of Functional Analysis</i>, vol. 282, no. 8. Elsevier, 2022.","ama":"Cipolloni G, Erdös L, Schröder DJ. Thermalisation for Wigner matrices. <i>Journal of Functional Analysis</i>. 2022;282(8). doi:<a href=\"https://doi.org/10.1016/j.jfa.2022.109394\">10.1016/j.jfa.2022.109394</a>"},"date_published":"2022-04-15T00:00:00Z","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"       282","issue":"8","author":[{"full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","orcid":"0000-0002-2904-1856"}],"day":"15","ddc":["500"],"oa":1,"article_processing_charge":"Yes (via OA deal)","publication_status":"published","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.","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"}],"title":"Thermalisation for Wigner matrices","publication_identifier":{"eissn":["1096-0783"],"issn":["0022-1236"]},"file":[{"access_level":"open_access","content_type":"application/pdf","success":1,"creator":"dernst","file_size":652573,"date_updated":"2022-07-29T07:22:08Z","date_created":"2022-07-29T07:22:08Z","checksum":"b75fdad606ab507dc61109e0907d86c0","file_name":"2022_JourFunctionalAnalysis_Cipolloni.pdf","relation":"main_file","file_id":"11690"}],"isi":1,"publication":"Journal of Functional Analysis","year":"2022","article_type":"original","external_id":{"arxiv":["2102.09975"],"isi":["000781239100004"]},"language":[{"iso":"eng"}]},{"type":"journal_article","scopus_import":"1","project":[{"call_identifier":"FP7","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems"}],"month":"05","_id":"15013","oa_version":"Preprint","date_updated":"2025-04-15T08:05:02Z","volume":2,"quality_controlled":"1","date_created":"2024-02-18T23:01:03Z","doi":"10.2140/pmp.2021.2.221","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1907.13631"}],"department":[{"_id":"LaEr"}],"publisher":"Mathematical Sciences Publishers","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","intvolume":"         2","citation":{"ama":"Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent entries. <i>Probability and Mathematical Physics</i>. 2021;2(2):221-280. doi:<a href=\"https://doi.org/10.2140/pmp.2021.2.221\">10.2140/pmp.2021.2.221</a>","apa":"Alt, J., Erdös, L., &#38; Krüger, T. H. (2021). Spectral radius of random matrices with independent entries. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2021.2.221\">https://doi.org/10.2140/pmp.2021.2.221</a>","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with independent entries,” <i>Probability and Mathematical Physics</i>, vol. 2, no. 2. Mathematical Sciences Publishers, pp. 221–280, 2021.","ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.","mla":"Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent Entries.” <i>Probability and Mathematical Physics</i>, vol. 2, no. 2, Mathematical Sciences Publishers, 2021, pp. 221–80, doi:<a href=\"https://doi.org/10.2140/pmp.2021.2.221\">10.2140/pmp.2021.2.221</a>.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random Matrices with Independent Entries.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/pmp.2021.2.221\">https://doi.org/10.2140/pmp.2021.2.221</a>.","short":"J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021) 221–280."},"date_published":"2021-05-21T00:00:00Z","arxiv":1,"corr_author":"1","status":"public","ec_funded":1,"article_processing_charge":"No","oa":1,"author":[{"first_name":"Johannes","full_name":"Alt, Johannes","last_name":"Alt","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","first_name":"Torben H"}],"day":"21","issue":"2","title":"Spectral radius of random matrices with independent entries","abstract":[{"lang":"eng","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."}],"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.","publication_status":"published","page":"221-280","publication":"Probability and Mathematical Physics","publication_identifier":{"eissn":["2690-1005"],"issn":["2690-0998"]},"external_id":{"arxiv":["1907.13631"]},"language":[{"iso":"eng"}],"year":"2021","article_type":"original"},{"keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"type":"journal_article","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1904.04312"}],"doi":"10.1214/20-aop1496","_id":"15259","month":"07","oa_version":"Preprint","volume":49,"date_created":"2024-04-03T07:19:42Z","quality_controlled":"1","date_updated":"2025-09-10T10:13:20Z","scopus_import":"1","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","grant_number":"754411"}],"publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"corr_author":"1","status":"public","ec_funded":1,"arxiv":1,"citation":{"short":"G. Dubach, Y. Peled, The Annals of Probability 49 (2021) 1886–1916.","chicago":"Dubach, Guillaume, and Yuval Peled. “On Words of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>. Institute of Mathematical Statistics, 2021. <a href=\"https://doi.org/10.1214/20-aop1496\">https://doi.org/10.1214/20-aop1496</a>.","mla":"Dubach, Guillaume, and Yuval Peled. “On Words of Non-Hermitian Random Matrices.” <i>The Annals of Probability</i>, vol. 49, no. 4, Institute of Mathematical Statistics, 2021, pp. 1886–916, doi:<a href=\"https://doi.org/10.1214/20-aop1496\">10.1214/20-aop1496</a>.","ista":"Dubach G, Peled Y. 2021. On words of non-Hermitian random matrices. The Annals of Probability. 49(4), 1886–1916.","ieee":"G. Dubach and Y. Peled, “On words of non-Hermitian random matrices,” <i>The Annals of Probability</i>, vol. 49, no. 4. Institute of Mathematical Statistics, pp. 1886–1916, 2021.","apa":"Dubach, G., &#38; Peled, Y. (2021). On words of non-Hermitian random matrices. <i>The Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/20-aop1496\">https://doi.org/10.1214/20-aop1496</a>","ama":"Dubach G, Peled Y. On words of non-Hermitian random matrices. <i>The Annals of Probability</i>. 2021;49(4):1886-1916. doi:<a href=\"https://doi.org/10.1214/20-aop1496\">10.1214/20-aop1496</a>"},"date_published":"2021-07-01T00:00:00Z","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","intvolume":"        49","issue":"4","author":[{"full_name":"Dubach, Guillaume","first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach","orcid":"0000-0001-6892-8137"},{"last_name":"Peled","full_name":"Peled, Yuval","first_name":"Yuval"}],"day":"01","oa":1,"article_processing_charge":"No","publication_status":"published","page":"1886-1916","acknowledgement":"The authors would like to thank Gernot Akemann, Benson Au, Paul Bourgade, Jesper Ipsen, Camille Male, Jamie Mingo, Doron Puder, Emily Redelmeier, Roland Speicher, Wojciech Tarnowski and Ofer Zeitouni for useful discussions, comments and references as well as the anonymous referee for a suggestion that greatly improved one of the theorems.\r\nG.D. gratefully acknowledges support from the grants NSF DMS-1812114 of P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI), as well as the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411.","abstract":[{"text":"We consider words Gi1⋯Gim involving i.i.d. complex Ginibre matrices and study tracial expressions of their eigenvalues and singular values. We show that the limit distribution of the squared singular values of every word of length m is a Fuss–Catalan distribution with parameter \r\nm+1. This generalizes previous results concerning powers of a complex Ginibre matrix and products of independent Ginibre matrices. In addition, we find other combinatorial parameters of the word that determine the second-order limits of the spectral statistics. For instance, the so-called coperiod of a word characterizes the fluctuations of the eigenvalues. We extend these results to words of general non-Hermitian matrices with i.i.d. entries under moment-matching assumptions, band matrices, and sparse matrices.\r\nThese results rely on the moments method and genus expansion, relating Gaussian matrix integrals to the counting of compact orientable surfaces of a given genus. This allows us to derive a central limit theorem for the trace of any word of complex Ginibre matrices and their conjugate transposes, where all parameters are defined topologically.","lang":"eng"}],"title":"On words of non-Hermitian random matrices","publication_identifier":{"issn":["0091-1798"]},"isi":1,"publication":"The Annals of Probability","year":"2021","article_type":"original","external_id":{"isi":["000681349000008"],"arxiv":["1904.04312"]},"language":[{"iso":"eng"}]},{"department":[{"_id":"LaEr"}],"file_date_updated":"2022-02-02T10:19:55Z","publisher":"Springer Nature","date_published":"2021-10-29T00:00:00Z","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Eigenstate thermalization hypothesis for Wigner matrices. <i>Communications in Mathematical Physics</i>. 2021;388(2):1005–1048. doi:<a href=\"https://doi.org/10.1007/s00220-021-04239-z\">10.1007/s00220-021-04239-z</a>","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Eigenstate thermalization hypothesis for Wigner matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04239-z\">https://doi.org/10.1007/s00220-021-04239-z</a>","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis for Wigner matrices,” <i>Communications in Mathematical Physics</i>, vol. 388, no. 2. Springer Nature, pp. 1005–1048, 2021.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <i>Communications in Mathematical Physics</i>, vol. 388, no. 2, Springer Nature, 2021, pp. 1005–1048, doi:<a href=\"https://doi.org/10.1007/s00220-021-04239-z\">10.1007/s00220-021-04239-z</a>.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04239-z\">https://doi.org/10.1007/s00220-021-04239-z</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048."},"intvolume":"       388","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","corr_author":"1","status":"public","arxiv":1,"has_accepted_license":"1","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"type":"journal_article","date_updated":"2025-04-15T06:53:08Z","volume":388,"date_created":"2021-11-07T23:01:25Z","quality_controlled":"1","_id":"10221","month":"10","oa_version":"Published Version","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"scopus_import":"1","doi":"10.1007/s00220-021-04239-z","publication":"Communications in Mathematical Physics","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"isi":1,"file":[{"success":1,"creator":"cchlebak","file_size":841426,"date_created":"2022-02-02T10:19:55Z","date_updated":"2022-02-02T10:19:55Z","content_type":"application/pdf","access_level":"open_access","file_name":"2021_CommunMathPhys_Cipolloni.pdf","file_id":"10715","relation":"main_file","checksum":"a2c7b6f5d23b5453cd70d1261272283b"}],"language":[{"iso":"eng"}],"external_id":{"arxiv":["2012.13215"],"isi":["000712232700001"]},"article_type":"original","year":"2021","oa":1,"article_processing_charge":"Yes (via OA deal)","issue":"2","ddc":["510"],"day":"29","author":[{"orcid":"0000-0002-4901-7992","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"first_name":"Dominik J","full_name":"Schröder, Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"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","page":"1005–1048","publication_status":"published","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria)."},{"publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"file_date_updated":"2021-11-15T10:10:17Z","article_number":"124","ec_funded":1,"status":"public","intvolume":"        26","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","citation":{"ieee":"G. Dubach, “On eigenvector statistics in the spherical and truncated unitary ensembles,” <i>Electronic Journal of Probability</i>, vol. 26. Institute of Mathematical Statistics, 2021.","apa":"Dubach, G. (2021). On eigenvector statistics in the spherical and truncated unitary ensembles. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-EJP686\">https://doi.org/10.1214/21-EJP686</a>","ama":"Dubach G. On eigenvector statistics in the spherical and truncated unitary ensembles. <i>Electronic Journal of Probability</i>. 2021;26. doi:<a href=\"https://doi.org/10.1214/21-EJP686\">10.1214/21-EJP686</a>","chicago":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2021. <a href=\"https://doi.org/10.1214/21-EJP686\">https://doi.org/10.1214/21-EJP686</a>.","short":"G. Dubach, Electronic Journal of Probability 26 (2021).","mla":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” <i>Electronic Journal of Probability</i>, vol. 26, 124, Institute of Mathematical Statistics, 2021, doi:<a href=\"https://doi.org/10.1214/21-EJP686\">10.1214/21-EJP686</a>.","ista":"Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 26, 124."},"date_published":"2021-09-28T00:00:00Z","type":"journal_article","tmp":{"image":"/images/cc_by.png","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"has_accepted_license":"1","doi":"10.1214/21-EJP686","project":[{"grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"scopus_import":"1","date_updated":"2025-04-14T07:43:47Z","date_created":"2021-11-14T23:01:25Z","volume":26,"quality_controlled":"1","month":"09","_id":"10285","oa_version":"Published Version","file":[{"checksum":"1c975afb31460277ce4d22b93538e5f9","relation":"main_file","file_id":"10288","file_name":"2021_ElecJournalProb_Dubach.pdf","access_level":"open_access","content_type":"application/pdf","file_size":735940,"date_updated":"2021-11-15T10:10:17Z","date_created":"2021-11-15T10:10:17Z","creator":"cchlebak","success":1}],"publication_identifier":{"eissn":["1083-6489"]},"publication":"Electronic Journal of Probability","article_type":"original","year":"2021","language":[{"iso":"eng"}],"day":"28","ddc":["519"],"author":[{"orcid":"0000-0001-6892-8137","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach","full_name":"Dubach, Guillaume","first_name":"Guillaume"}],"article_processing_charge":"No","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.","publication_status":"published","title":"On eigenvector statistics in the spherical and truncated unitary ensembles","abstract":[{"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.","lang":"eng"}]}]