[{"publication":"Communications in Mathematical Physics","intvolume":"       407","citation":{"apa":"Jain, V., Kwan, M. A., &#38; Michelen, M. (2026). Entangled states are typically incomparable. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-026-05711-4\">https://doi.org/10.1007/s00220-026-05711-4</a>","mla":"Jain, Vishesh, et al. “Entangled States Are Typically Incomparable.” <i>Communications in Mathematical Physics</i>, vol. 407, no. 10, 214, Springer, 2026, doi:<a href=\"https://doi.org/10.1007/s00220-026-05711-4\">10.1007/s00220-026-05711-4</a>.","ista":"Jain V, Kwan MA, Michelen M. 2026. Entangled states are typically incomparable. Communications in Mathematical Physics. 407(10), 214.","chicago":"Jain, Vishesh, Matthew Alan Kwan, and Marcus Michelen. “Entangled States Are Typically Incomparable.” <i>Communications in Mathematical Physics</i>. Springer, 2026. <a href=\"https://doi.org/10.1007/s00220-026-05711-4\">https://doi.org/10.1007/s00220-026-05711-4</a>.","ieee":"V. Jain, M. A. Kwan, and M. Michelen, “Entangled states are typically incomparable,” <i>Communications in Mathematical Physics</i>, vol. 407, no. 10. Springer, 2026.","ama":"Jain V, Kwan MA, Michelen M. Entangled states are typically incomparable. <i>Communications in Mathematical Physics</i>. 2026;407(10). doi:<a href=\"https://doi.org/10.1007/s00220-026-05711-4\">10.1007/s00220-026-05711-4</a>","short":"V. Jain, M.A. Kwan, M. Michelen, Communications in Mathematical Physics 407 (2026)."},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","language":[{"iso":"eng"}],"external_id":{"arxiv":["2406.03335"],"pmid":["42668663"]},"abstract":[{"text":"Consider a bipartite quantum system, where Alice and Bob jointly possess\r\na pure state |ψ\u0002. Using local quantum operations on their respective subsystems, and\r\nunlimited classical communication, Alice and Bob may be able to transform |ψ\u0002 into\r\nanother state |φ\u0002. Famously, Nielsen’s theorem [28] provides a necessary and sufficient\r\nalgebraic criterion for such a transformation to be possible (namely, the entanglement\r\nspectrum of |φ\u0002 should majorise the entanglement spectrum of |ψ\u0002). In the paper where\r\nNielsen proved this theorem, he conjectured that in the limit of large dimensionality, for\r\nalmost all pairs of states |ψ\u0002, |φ\u0002 (according to the natural unitary invariant measure) such\r\na transformation is not possible. That is to say, typical pairs of quantum states |ψ\u0002, |φ\u0002\r\nare entangled in fundamentally different ways, that cannot be converted to each other via\r\nlocal operations and classical communication.ViaNielsen’s theorem, this conjecture can\r\nbe equivalently stated as a conjecture about majorisation of spectra of random matrices\r\nfrom the so-called trace-normalised complex Wishart–Laguerre ensemble. Concretely,\r\nlet X and Y be independent n × m random matrices whose entries are i.i.d. standard\r\ncomplex Gaussians; then Nielsen’s conjecture says that the probability that the spectrum\r\nof XX†/ tr(XX†) majorises the spectrum of YY†/ tr(YY†) tends to zero as both n and\r\nm grow large. We prove this conjecture, and we also confirm some related predictions\r\nof Cunden et al. [12].","lang":"eng"}],"author":[{"first_name":"Vishesh","full_name":"Jain, Vishesh","last_name":"Jain"},{"orcid":"0000-0002-4003-7567","id":"5fca0887-a1db-11eb-95d1-ca9d5e0453b3","first_name":"Matthew Alan","full_name":"Kwan, Matthew Alan","last_name":"Kwan"},{"last_name":"Michelen","first_name":"Marcus","full_name":"Michelen, Marcus"}],"file_date_updated":"2026-09-09T12:32:53Z","article_number":"214","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"oa_version":"Published Version","publication_status":"published","date_created":"2026-09-06T22:01:56Z","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00220-026-05711-4","_id":"22813","supplementarymaterial":"no","publisher":"Springer","article_type":"original","title":"Entangled states are typically incomparable","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"volume":407,"month":"08","oa":1,"das_tickbox":"1","OA_place":"publisher","date_published":"2026-08-28T00:00:00Z","arxiv":1,"year":"2026","file":[{"date_updated":"2026-09-09T12:32:53Z","creator":"dernst","content_type":"application/pdf","relation":"main_file","file_name":"2026_CommMathPhysics_Jain.pdf","success":1,"access_level":"open_access","file_id":"22888","date_created":"2026-09-09T12:32:53Z","checksum":"61c226b6314a88db25e864e4218d5de3","file_size":463477}],"PlanS_conform":"1","dataavailabilitystatement":"No datasets were used in this research.","department":[{"_id":"MaKw"}],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Vishesh Jain was partially supported by NSF CAREER award DMS-2237646. Matthew Kwan was supported by ERC Starting Grant “RANDSTRUCT” No. 101076777. Marcus Michelen was supported in part by NSF grants DMS-2137623 and DMS-2246624.","quality_controlled":"1","OA_type":"hybrid","researchdata_availability":"no","date_updated":"2026-09-09T12:35:24Z","day":"28","pmid":1,"fulldoi":"https://doi.org/10.1007/s00220-026-05711-4","scopus_import":"1","ddc":["500"],"type":"journal_article","license":"https://creativecommons.org/licenses/by/4.0/","status":"public","has_accepted_license":"1","project":[{"_id":"bd95085b-d553-11ed-ba76-e55d3349be45","name":"Randomness and structure in combinatorics","grant_number":"101076777"}],"issue":"10"},{"date_published":"2025-05-01T00:00:00Z","OA_place":"publisher","oa":1,"volume":406,"month":"05","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"title":"Operator-valued twisted Araki–Woods algebras","article_type":"original","publisher":"Springer Nature","_id":"19625","publication_status":"published","date_created":"2025-04-27T22:02:13Z","doi":"10.1007/s00220-025-05285-7","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"article_number":"110","file_date_updated":"2025-05-05T09:20:54Z","author":[{"first_name":"R. Rahul","full_name":"Kumar, R. Rahul","last_name":"Kumar"},{"first_name":"Melchior","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","last_name":"Wirth"}],"abstract":[{"lang":"eng","text":"We introduce operator-valued twisted Araki–Woods algebras. These are operator-valued versions of a class of second quantization algebras that includes q-Gaussian and q-Araki–Woods algebras and also generalize Shlyakhtenko’s von Neumann algebras generated by operator-valued semicircular variables. We develop a disintegration theory that reduces the isomorphism type of operator-valued twisted Araki–Woods algebras over type I factors to the scalar-valued case. Moreover, these algebras come with a natural weight, and we characterize its modular theory. We also give sufficient criteria that guarantee the factoriality of these algebras."}],"external_id":{"pmid":["40225194"],"arxiv":["2406.06179"],"isi":["001464170400003"]},"language":[{"iso":"eng"}],"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","isi":1,"citation":{"mla":"Kumar, R. Rahul, and Melchior Wirth. “Operator-Valued Twisted Araki–Woods Algebras.” <i>Communications in Mathematical Physics</i>, vol. 406, no. 5, 110, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00220-025-05285-7\">10.1007/s00220-025-05285-7</a>.","apa":"Kumar, R. R., &#38; Wirth, M. (2025). Operator-valued twisted Araki–Woods algebras. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-025-05285-7\">https://doi.org/10.1007/s00220-025-05285-7</a>","chicago":"Kumar, R. Rahul, and Melchior Wirth. “Operator-Valued Twisted Araki–Woods Algebras.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00220-025-05285-7\">https://doi.org/10.1007/s00220-025-05285-7</a>.","ieee":"R. R. Kumar and M. Wirth, “Operator-valued twisted Araki–Woods algebras,” <i>Communications in Mathematical Physics</i>, vol. 406, no. 5. Springer Nature, 2025.","ista":"Kumar RR, Wirth M. 2025. Operator-valued twisted Araki–Woods algebras. Communications in Mathematical Physics. 406(5), 110.","ama":"Kumar RR, Wirth M. Operator-valued twisted Araki–Woods algebras. <i>Communications in Mathematical Physics</i>. 2025;406(5). doi:<a href=\"https://doi.org/10.1007/s00220-025-05285-7\">10.1007/s00220-025-05285-7</a>","short":"R.R. Kumar, M. Wirth, Communications in Mathematical Physics 406 (2025)."},"intvolume":"       406","publication":"Communications in Mathematical Physics","issue":"5","project":[{"grant_number":"ESP156_N","name":"Gradient flow techniques for quantum Markov semigroups","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833"}],"has_accepted_license":"1","status":"public","type":"journal_article","ddc":["510"],"scopus_import":"1","pmid":1,"fulldoi":"https://doi.org/10.1007/s00220-025-05285-7","date_updated":"2025-09-30T12:19:22Z","day":"01","OA_type":"hybrid","quality_controlled":"1","acknowledgement":"The authors want to thank the organizers of YMC*A 2023 in Leuven, where this collaboration was conceived. They are grateful to Dan Voiculescu for a valuable historical remark and to Zhiyuan Yang for raising the question if operator-valued weights give rise to Tomita correspondences. R.K. was funded by IIT Kanpur through the Institute Postdoctoral Fellowship. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission.\r\nOpen Access funding enabled and organized by Projekt DEAL.","department":[{"_id":"JaMa"}],"file":[{"date_updated":"2025-05-05T09:20:54Z","content_type":"application/pdf","file_name":"2025_CommMathPhysics_Kumar.pdf","relation":"main_file","creator":"dernst","success":1,"file_size":650764,"file_id":"19650","access_level":"open_access","date_created":"2025-05-05T09:20:54Z","checksum":"2948e8f567f20f5f837061d2c775534f"}],"year":"2025","arxiv":1},{"fulldoi":"https://doi.org/10.1007/s00220-025-05417-z","date_updated":"2026-04-07T12:32:19Z","day":"01","scopus_import":"1","ddc":["510"],"type":"journal_article","has_accepted_license":"1","status":"public","issue":"10","arxiv":1,"file":[{"relation":"main_file","file_name":"2025_CommMathPhysics_Erdoes.pdf","content_type":"application/pdf","creator":"dernst","date_updated":"2025-09-10T07:48:21Z","file_size":1465827,"checksum":"abd32af7b8ca6dc5b9080823a433986b","date_created":"2025-09-10T07:48:21Z","access_level":"open_access","file_id":"20336","success":1}],"PlanS_conform":"1","year":"2025","department":[{"_id":"LaEr"}],"acknowledgement":"We thank Giorgio Cipolloni for many productive discussions and the anonymous referees for several useful suggestions and spotting some typos. Open access funding provided by Institute of Science and Technology (IST Austria).","OA_type":"hybrid","quality_controlled":"1","_id":"20322","publisher":"Springer Nature","article_type":"original","title":"Cusp universality for correlated random matrices","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"09","volume":406,"date_published":"2025-09-01T00:00:00Z","OA_place":"publisher","oa":1,"intvolume":"       406","citation":{"apa":"Erdös, L., Henheik, S. J., &#38; Riabov, V. (2025). Cusp universality for correlated random matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-025-05417-z\">https://doi.org/10.1007/s00220-025-05417-z</a>","mla":"Erdös, László, et al. “Cusp Universality for Correlated Random Matrices.” <i>Communications in Mathematical Physics</i>, vol. 406, no. 10, 253, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00220-025-05417-z\">10.1007/s00220-025-05417-z</a>.","ieee":"L. Erdös, S. J. Henheik, and V. Riabov, “Cusp universality for correlated random matrices,” <i>Communications in Mathematical Physics</i>, vol. 406, no. 10. Springer Nature, 2025.","ista":"Erdös L, Henheik SJ, Riabov V. 2025. Cusp universality for correlated random matrices. Communications in Mathematical Physics. 406(10), 253.","chicago":"Erdös, László, Sven Joscha Henheik, and Volodymyr Riabov. “Cusp Universality for Correlated Random Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00220-025-05417-z\">https://doi.org/10.1007/s00220-025-05417-z</a>.","short":"L. Erdös, S.J. Henheik, V. Riabov, Communications in Mathematical Physics 406 (2025).","ama":"Erdös L, Henheik SJ, Riabov V. Cusp universality for correlated random matrices. <i>Communications in Mathematical Physics</i>. 2025;406(10). doi:<a href=\"https://doi.org/10.1007/s00220-025-05417-z\">10.1007/s00220-025-05417-z</a>"},"publication":"Communications in Mathematical Physics","corr_author":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","isi":1,"related_material":{"record":[{"id":"19547","status":"public","relation":"earlier_version"},{"relation":"dissertation_contains","id":"20575","status":"public"}]},"language":[{"iso":"eng"}],"author":[{"full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","last_name":"Henheik"},{"id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr","first_name":"Volodymyr","last_name":"Riabov"}],"abstract":[{"text":"For correlated real symmetric or complex Hermitian random matrices, we prove that the local eigenvalue statistics at any cusp singularity are universal. Since the density of states typically exhibits only square root edge or cubic root cusp singularities, our result completes the proof of the Wigner–Dyson–Mehta universality conjecture in all spectral regimes for a very general class of random matrices. Previously only the bulk and the edge universality were established in this generality (Alt et al. in Ann Probab 48(2):963–1001, 2020), while cusp universality was proven only for Wigner-type matrices with independent entries (Cipolloni et al. in Pure Appl Anal 1:615–707, 2019; Erdős et al. in Commun. Math. Phys. 378:1203–1278, 2018). As our main technical input, we prove an optimal local law at the cusp using the <jats:italic>Zigzag strategy</jats:italic>, a recursive tandem of the characteristic flow method and a Green function comparison argument. Moreover, our proof of the optimal local law holds uniformly in the spectrum, thus we also provide a significantly simplified alternative proof of the local eigenvalue universality in the previously studied bulk (Erdős et al. in Forum Math. Sigma 7:E8, 2019) and edge (Alt et al. in Ann Probab 48(2):963–1001, 2020) regimes.","lang":"eng"}],"external_id":{"arxiv":["2410.06813"],"isi":["001565019000005"]},"article_number":"253","file_date_updated":"2025-09-10T07:48:21Z","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa_version":"Published Version","doi":"10.1007/s00220-025-05417-z","date_created":"2025-09-10T05:38:17Z","publication_status":"published","article_processing_charge":"Yes (via OA deal)"},{"arxiv":1,"file":[{"success":1,"date_created":"2024-05-06T06:18:45Z","access_level":"open_access","file_id":"15365","checksum":"8ecd168755f0d40ebd7cd0b71063acfc","file_size":653676,"date_updated":"2024-05-06T06:18:45Z","creator":"dernst","content_type":"application/pdf","relation":"main_file","file_name":"2024_CommMathPhysics_Rouze.pdf"}],"year":"2024","department":[{"_id":"JaMa"}],"dataavailabilitystatement":"No data was generated as part of this work.","acknowledgement":"Open access funding provided by the Carolinas Consortium.\r\nH.Z. is supported by the Lise Meitner fellowship, Austrian Science Fund (FWF) M3337. H.Z. would like to thank the American Institute of Mathematics and the AIM workshop Analysis on the hypercube with applications to quantum computing. He is also grateful to the organizers and other participants for creating an active atmosphere. The research of C.R. has been supported by ANR project QTraj (ANR-20-CE40-0024-01) of the French National Research Agency (ANR). C.R. acknowledges the support of the Munich Center for Quantum Sciences and Technology, as well as the Humboldt Foundation. C.R. would like to thank Amanda Young for fruitful discussion on the applications of Friedgut’s Junta theorem to learning quantum dynamics. The research of M.W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. The authors want to thank Francisco Escudero Gutierrez and Hsin-Yuan Huang for helpful comments on an earlier version of the paper. They are grateful to the referees for the careful reading and helpful comments.","researchdata_availability":"not applicable","quality_controlled":"1","fulldoi":"https://doi.org/10.1007/s00220-024-04981-0","pmid":1,"date_updated":"2026-10-02T12:16:36Z","day":"09","scopus_import":"1","ddc":["510"],"type":"journal_article","has_accepted_license":"1","status":"public","issue":"4","project":[{"_id":"eb958bca-77a9-11ec-83b8-c565cb50d8d6","name":"Curvature-dimension in noncommutative analysis","grant_number":"M03337"},{"_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833","grant_number":"ESP156_N","name":"Gradient flow techniques for quantum Markov semigroups"}],"intvolume":"       405","citation":{"mla":"Rouzé, Cambyse, et al. “Quantum Talagrand, KKL and Friedgut’s Theorems and the Learnability of Quantum Boolean Functions.” <i>Communications in Mathematical Physics</i>, vol. 405, no. 4, 95, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00220-024-04981-0\">10.1007/s00220-024-04981-0</a>.","apa":"Rouzé, C., Wirth, M., &#38; Zhang, H. (2024). Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum boolean functions. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-024-04981-0\">https://doi.org/10.1007/s00220-024-04981-0</a>","short":"C. Rouzé, M. Wirth, H. Zhang, Communications in Mathematical Physics 405 (2024).","ama":"Rouzé C, Wirth M, Zhang H. Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum boolean functions. <i>Communications in Mathematical Physics</i>. 2024;405(4). doi:<a href=\"https://doi.org/10.1007/s00220-024-04981-0\">10.1007/s00220-024-04981-0</a>","ieee":"C. Rouzé, M. Wirth, and H. Zhang, “Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum boolean functions,” <i>Communications in Mathematical Physics</i>, vol. 405, no. 4. Springer Nature, 2024.","chicago":"Rouzé, Cambyse, Melchior Wirth, and Haonan Zhang. “Quantum Talagrand, KKL and Friedgut’s Theorems and the Learnability of Quantum Boolean Functions.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00220-024-04981-0\">https://doi.org/10.1007/s00220-024-04981-0</a>.","ista":"Rouzé C, Wirth M, Zhang H. 2024. Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum boolean functions. Communications in Mathematical Physics. 405(4), 95."},"publication":"Communications in Mathematical Physics","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","isi":1,"language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"We extend three related results from the analysis of influences of Boolean functions to the quantum setting, namely the KKL theorem, Friedgut’s Junta theorem and Talagrand’s variance inequality for geometric influences. Our results are derived by a joint use of recently studied hypercontractivity and gradient estimates. These generic tools also allow us to derive generalizations of these results in a general von Neumann algebraic setting beyond the case of the quantum hypercube, including examples in infinite dimensions relevant to quantum information theory such as continuous variables quantum systems. Finally, we comment on the implications of our results as regards to noncommutative extensions of isoperimetric type inequalities, quantum circuit complexity lower bounds and the learnability of quantum observables."}],"author":[{"last_name":"Rouzé","full_name":"Rouzé, Cambyse","first_name":"Cambyse"},{"last_name":"Wirth","orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E","first_name":"Melchior","full_name":"Wirth, Melchior"},{"first_name":"Haonan","full_name":"Zhang, Haonan","orcid":"0000-0001-9537-9663","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","last_name":"Zhang"}],"external_id":{"pmid":["38606337"],"arxiv":["2209.07279"],"isi":["001199509500004"]},"article_number":"95","file_date_updated":"2024-05-06T06:18:45Z","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa_version":"Published Version","date_created":"2024-04-29T08:47:28Z","doi":"10.1007/s00220-024-04981-0","article_processing_charge":"Yes (via OA deal)","publication_status":"published","_id":"15350","supplementarymaterial":"no","publisher":"Springer Nature","article_type":"original","title":"Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum boolean functions","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"04","volume":405,"date_published":"2024-04-09T00:00:00Z","das_tickbox":"1","oa":1},{"isi":1,"user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","corr_author":"1","language":[{"iso":"eng"}],"related_material":{"record":[{"id":"20575","status":"public","relation":"dissertation_contains"}]},"publication":"Communications in Mathematical Physics","intvolume":"       405","citation":{"mla":"Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” <i>Communications in Mathematical Physics</i>, vol. 405, no. 12, 282, Springer Nature, 2024, doi:<a href=\"https://doi.org/10.1007/s00220-024-05143-y\">10.1007/s00220-024-05143-y</a>.","apa":"Erdös, L., &#38; Riabov, V. (2024). Eigenstate Thermalization Hypothesis for Wigner-type matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-024-05143-y\">https://doi.org/10.1007/s00220-024-05143-y</a>","chicago":"Erdös, László, and Volodymyr Riabov. “Eigenstate Thermalization Hypothesis for Wigner-Type Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00220-024-05143-y\">https://doi.org/10.1007/s00220-024-05143-y</a>.","ieee":"L. Erdös and V. Riabov, “Eigenstate Thermalization Hypothesis for Wigner-type matrices,” <i>Communications in Mathematical Physics</i>, vol. 405, no. 12. Springer Nature, 2024.","ista":"Erdös L, Riabov V. 2024. Eigenstate Thermalization Hypothesis for Wigner-type matrices. Communications in Mathematical Physics. 405(12), 282.","short":"L. Erdös, V. Riabov, Communications in Mathematical Physics 405 (2024).","ama":"Erdös L, Riabov V. Eigenstate Thermalization Hypothesis for Wigner-type matrices. <i>Communications in Mathematical Physics</i>. 2024;405(12). doi:<a href=\"https://doi.org/10.1007/s00220-024-05143-y\">10.1007/s00220-024-05143-y</a>"},"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa_version":"Published Version","date_created":"2024-11-17T23:01:46Z","publication_status":"published","doi":"10.1007/s00220-024-05143-y","article_processing_charge":"Yes (via OA deal)","external_id":{"pmid":["39526190"],"arxiv":["2403.10359"],"isi":["001348943900004"]},"abstract":[{"lang":"eng","text":"We prove the Eigenstate Thermalization Hypothesis for general Wigner-type matrices in the bulk of the self-consistent spectrum, with optimal control on the fluctuations for obs ervables of arbitrary rank. As the main technical ingredient, we prove rank-uniform optimal local laws for one and two resolvents of a Wigner-type matrix with regular observables. Our results hold under very general conditions on the variance profile, even allowing many vanishing entries, demonstrating that Eigenstate Thermalization occurs robustly across a diverse class of random matrix ensembles, for which the underlying quantum system has a non-trivial spatial structure."}],"author":[{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"id":"1949f904-edfb-11eb-afb5-e2dfddabb93b","full_name":"Riabov, Volodymyr","first_name":"Volodymyr","last_name":"Riabov"}],"file_date_updated":"2024-11-18T08:15:07Z","article_number":"282","article_type":"original","title":"Eigenstate Thermalization Hypothesis for Wigner-type matrices","supplementarymaterial":"yes","_id":"18554","publisher":"Springer Nature","month":"12","volume":405,"oa":1,"das_tickbox":"1","OA_place":"publisher","date_published":"2024-12-01T00:00:00Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"year":"2024","file":[{"date_updated":"2024-11-18T08:15:07Z","content_type":"application/pdf","relation":"main_file","file_name":"2024_CommMathPhysics_Erdoes.pdf","creator":"dernst","success":1,"file_size":1426046,"date_created":"2024-11-18T08:15:07Z","file_id":"18562","access_level":"open_access","checksum":"c9ae0ea195bd39b8b3a630d492fb00dc"}],"dataavailabilitystatement":"There is no data associated to this work.","department":[{"_id":"LaEr"}],"arxiv":1,"quality_controlled":"1","OA_type":"hybrid","researchdata_availability":"not applicable","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","scopus_import":"1","ddc":["510"],"date_updated":"2026-10-16T08:34:30Z","day":"01","fulldoi":"https://doi.org/10.1007/s00220-024-05143-y","pmid":1,"issue":"12","type":"journal_article","status":"public","has_accepted_license":"1"},{"quality_controlled":"1","acknowledgement":"We are grateful to the authors of [25] for sharing with us their insights and preliminary numerical results. We are especially thankful to Stephen Shenker for very valuable advice over several email communications. Helpful comments on the manuscript from Peter Forrester and from the anonymous referees are also acknowledged.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).\r\nLászló Erdős: Partially supported by ERC Advanced Grant \"RMTBeyond\" No. 101020331. Dominik Schröder: Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","year":"2023","file":[{"creator":"dernst","content_type":"application/pdf","relation":"main_file","file_name":"2023_CommMathPhysics_Cipolloni.pdf","date_updated":"2023-10-04T12:09:18Z","access_level":"open_access","date_created":"2023-10-04T12:09:18Z","file_id":"14397","checksum":"72057940f76654050ca84a221f21786c","file_size":859967,"success":1}],"department":[{"_id":"LaEr"}],"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"page":"1665-1700","ec_funded":1,"type":"journal_article","status":"public","has_accepted_license":"1","scopus_import":"1","ddc":["510"],"date_updated":"2025-04-14T07:57:19Z","day":"01","fulldoi":"https://doi.org/10.1007/s00220-023-04692-y","oa_version":"Published Version","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00220-023-04692-y","date_created":"2023-04-02T22:01:11Z","publication_status":"published","external_id":{"isi":["000957343500001"]},"abstract":[{"lang":"eng","text":"In the physics literature the spectral form factor (SFF), the squared Fourier transform of the empirical eigenvalue density, is the most common tool to test universality for disordered quantum systems, yet previous mathematical results have been restricted only to two exactly solvable models (Forrester in J Stat Phys 183:33, 2021. https://doi.org/10.1007/s10955-021-02767-5, Commun Math Phys 387:215–235, 2021. https://doi.org/10.1007/s00220-021-04193-w). We rigorously prove the physics prediction on SFF up to an intermediate time scale for a large class of random matrices using a robust method, the multi-resolvent local laws. Beyond Wigner matrices we also consider the monoparametric ensemble and prove that universality of SFF can already be triggered by a single random parameter, supplementing the recently proven Wigner–Dyson universality (Cipolloni et al. in Probab Theory Relat Fields, 2021. https://doi.org/10.1007/s00440-022-01156-7) to larger spectral scales. Remarkably, extensive numerics indicates that our formulas correctly predict the SFF in the entire slope-dip-ramp regime, as customarily called in physics."}],"author":[{"last_name":"Cipolloni","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","first_name":"Dominik J","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"file_date_updated":"2023-10-04T12:09:18Z","isi":1,"corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","intvolume":"       401","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. On the spectral form factor for random matrices. <i>Communications in Mathematical Physics</i>. 2023;401:1665-1700. doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 401 (2023) 1665–1700.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. On the spectral form factor for random matrices. Communications in Mathematical Physics. 401, 1665–1700.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “On the spectral form factor for random matrices,” <i>Communications in Mathematical Physics</i>, vol. 401. Springer Nature, pp. 1665–1700, 2023.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). On the spectral form factor for random matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04692-y\">https://doi.org/10.1007/s00220-023-04692-y</a>","mla":"Cipolloni, Giorgio, et al. “On the Spectral Form Factor for Random Matrices.” <i>Communications in Mathematical Physics</i>, vol. 401, Springer Nature, 2023, pp. 1665–700, doi:<a href=\"https://doi.org/10.1007/s00220-023-04692-y\">10.1007/s00220-023-04692-y</a>."},"volume":401,"month":"07","oa":1,"date_published":"2023-07-01T00:00:00Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"article_type":"original","title":"On the spectral form factor for random matrices","_id":"12792","publisher":"Springer Nature"},{"corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"language":[{"iso":"eng"}],"intvolume":"       403","citation":{"apa":"Vernooij, M., &#38; Wirth, M. (2023). Derivations and KMS-symmetric quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04795-6\">https://doi.org/10.1007/s00220-023-04795-6</a>","mla":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 403, Springer Nature, 2023, pp. 381–416, doi:<a href=\"https://doi.org/10.1007/s00220-023-04795-6\">10.1007/s00220-023-04795-6</a>.","ama":"Vernooij M, Wirth M. Derivations and KMS-symmetric quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2023;403:381-416. doi:<a href=\"https://doi.org/10.1007/s00220-023-04795-6\">10.1007/s00220-023-04795-6</a>","short":"M. Vernooij, M. Wirth, Communications in Mathematical Physics 403 (2023) 381–416.","ista":"Vernooij M, Wirth M. 2023. Derivations and KMS-symmetric quantum Markov semigroups. Communications in Mathematical Physics. 403, 381–416.","ieee":"M. Vernooij and M. Wirth, “Derivations and KMS-symmetric quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 403. Springer Nature, pp. 381–416, 2023.","chicago":"Vernooij, Matthijs, and Melchior Wirth. “Derivations and KMS-Symmetric Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04795-6\">https://doi.org/10.1007/s00220-023-04795-6</a>."},"publication":"Communications in Mathematical Physics","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa_version":"Published Version","publication_status":"published","article_processing_charge":"Yes (via OA deal)","date_created":"2023-07-30T22:01:03Z","doi":"10.1007/s00220-023-04795-6","abstract":[{"lang":"eng","text":"We prove that the generator of the L2 implementation of a KMS-symmetric quantum Markov semigroup can be expressed as the square of a derivation with values in a Hilbert bimodule, extending earlier results by Cipriani and Sauvageot for tracially symmetric semigroups and the second-named author for GNS-symmetric semigroups. This result hinges on the introduction of a new completely positive map on the algebra of bounded operators on the GNS Hilbert space. This transformation maps symmetric Markov operators to symmetric Markov operators and is essential to obtain the required inner product on the Hilbert bimodule."}],"author":[{"full_name":"Vernooij, Matthijs","first_name":"Matthijs","last_name":"Vernooij"},{"last_name":"Wirth","full_name":"Wirth, Melchior","first_name":"Melchior","orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"}],"external_id":{"isi":["001033655400002"],"pmid":["37766789"],"arxiv":["2303.15949"]},"file_date_updated":"2024-01-30T12:15:11Z","article_type":"original","title":"Derivations and KMS-symmetric quantum Markov semigroups","_id":"13319","publisher":"Springer Nature","month":"10","volume":403,"date_published":"2023-10-01T00:00:00Z","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"success":1,"checksum":"cca204e81891270216a0c84eb8bcd398","access_level":"open_access","date_created":"2024-01-30T12:15:11Z","file_id":"14905","file_size":481209,"date_updated":"2024-01-30T12:15:11Z","creator":"dernst","relation":"main_file","file_name":"2023_CommMathPhysics_Vernooij.pdf","content_type":"application/pdf"}],"year":"2023","department":[{"_id":"JaMa"}],"arxiv":1,"quality_controlled":"1","acknowledgement":"The authors are grateful to Martijn Caspers for helpful comments on a preliminary version of this manuscript. M. V. was supported by the NWO Vidi grant VI.Vidi.192.018 ‘Non-commutative harmonic analysis and rigidity of operator algebras’. M. W. was funded by the Austrian Science Fund (FWF) under the Esprit Programme [ESP 156]. For the purpose of Open Access, the authors have applied a CC BY public copyright licence to any Author Accepted Manuscript (AAM) version arising from this submission. Open access funding provided by Austrian Science Fund (FWF).","scopus_import":"1","ddc":["510"],"pmid":1,"fulldoi":"https://doi.org/10.1007/s00220-023-04795-6","day":"01","date_updated":"2025-04-23T13:10:45Z","page":"381-416","project":[{"name":"Gradient flow techniques for quantum Markov semigroups","grant_number":"ESP156_N","_id":"34c6ea2d-11ca-11ed-8bc3-c04f3c502833"}],"type":"journal_article","has_accepted_license":"1","status":"public"},{"fulldoi":"https://doi.org/10.1007/s00220-023-04837-z","day":"01","date_updated":"2025-04-14T07:53:45Z","scopus_import":"1","type":"journal_article","status":"public","ec_funded":1,"page":"1-50","project":[{"grant_number":"885707","name":"Spectral rigidity and integrability for billiards and geodesic flows","call_identifier":"H2020","_id":"9B8B92DE-BA93-11EA-9121-9846C619BF3A"}],"arxiv":1,"year":"2023","department":[{"_id":"VaKa"}],"acknowledgement":"VK acknowledges a partial support by the NSF grant DMS-1402164 and ERC Grant #885707. Discussions with Martin Leguil and Jacopo De Simoi were very useful. JC visited the University of Maryland and thanks for the hospitality. Also, JC was partially supported by the National Key Research and Development Program of China (No.2022YFA1005802), the NSFC Grant 12001392 and NSF of Jiangsu BK20200850. H.-K. Zhang is partially supported by the National Science Foundation (DMS-2220211), as well as Simons Foundation Collaboration Grants for Mathematicians (706383).","quality_controlled":"1","_id":"14427","publisher":"Springer Nature","article_type":"original","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.07330"}],"title":"Length spectrum rigidity for piecewise analytic Bunimovich billiards","volume":404,"month":"11","date_published":"2023-11-01T00:00:00Z","oa":1,"citation":{"ista":"Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise analytic Bunimovich billiards. Communications in Mathematical Physics. 404, 1–50.","chicago":"Chen, Jianyu, Vadim Kaloshin, and Hong Kun Zhang. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04837-z\">https://doi.org/10.1007/s00220-023-04837-z</a>.","ieee":"J. Chen, V. Kaloshin, and H. K. Zhang, “Length spectrum rigidity for piecewise analytic Bunimovich billiards,” <i>Communications in Mathematical Physics</i>, vol. 404. Springer Nature, pp. 1–50, 2023.","ama":"Chen J, Kaloshin V, Zhang HK. Length spectrum rigidity for piecewise analytic Bunimovich billiards. <i>Communications in Mathematical Physics</i>. 2023;404:1-50. doi:<a href=\"https://doi.org/10.1007/s00220-023-04837-z\">10.1007/s00220-023-04837-z</a>","short":"J. Chen, V. Kaloshin, H.K. Zhang, Communications in Mathematical Physics 404 (2023) 1–50.","mla":"Chen, Jianyu, et al. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards.” <i>Communications in Mathematical Physics</i>, vol. 404, Springer Nature, 2023, pp. 1–50, doi:<a href=\"https://doi.org/10.1007/s00220-023-04837-z\">10.1007/s00220-023-04837-z</a>.","apa":"Chen, J., Kaloshin, V., &#38; Zhang, H. K. (2023). Length spectrum rigidity for piecewise analytic Bunimovich billiards. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04837-z\">https://doi.org/10.1007/s00220-023-04837-z</a>"},"intvolume":"       404","publication":"Communications in Mathematical Physics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","isi":1,"language":[{"iso":"eng"}],"abstract":[{"text":"In the paper, we establish Squash Rigidity Theorem—the dynamical spectral rigidity for piecewise analytic Bunimovich squash-type stadia whose convex arcs are homothetic. We also establish Stadium Rigidity Theorem—the dynamical spectral rigidity for piecewise analytic Bunimovich stadia whose flat boundaries are a priori fixed. In addition, for smooth Bunimovich squash-type stadia we compute the Lyapunov exponents along the maximal period two orbit, as well as the value of the Peierls’ Barrier function from the maximal marked length spectrum associated to the rotation number 2n/4n+1.","lang":"eng"}],"author":[{"first_name":"Jianyu","full_name":"Chen, Jianyu","last_name":"Chen"},{"last_name":"Kaloshin","first_name":"Vadim","full_name":"Kaloshin, Vadim","id":"FE553552-CDE8-11E9-B324-C0EBE5697425","orcid":"0000-0002-6051-2628"},{"full_name":"Zhang, Hong Kun","first_name":"Hong Kun","last_name":"Zhang"}],"external_id":{"isi":["001073177200001"],"arxiv":["1902.07330"]},"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"oa_version":"Preprint","article_processing_charge":"No","publication_status":"published","doi":"10.1007/s00220-023-04837-z","date_created":"2023-10-15T22:01:11Z"},{"scopus_import":"1","ddc":["510"],"date_updated":"2025-09-09T13:12:02Z","day":"01","fulldoi":"https://doi.org/10.1007/s00220-023-04841-3","project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"}],"page":"287-337","ec_funded":1,"type":"journal_article","status":"public","has_accepted_license":"1","year":"2023","file":[{"date_updated":"2023-10-31T12:21:39Z","creator":"dernst","content_type":"application/pdf","file_name":"2023_CommMathPhysics_Brooks.pdf","relation":"main_file","success":1,"access_level":"open_access","file_id":"14477","date_created":"2023-10-31T12:21:39Z","checksum":"1ae49b39247cb6b40ff75997381581b8","file_size":832375}],"department":[{"_id":"RoSe"}],"arxiv":1,"quality_controlled":"1","acknowledgement":"Funding from the European Union’s Horizon 2020 research and innovation programme under the ERC grant agreement No 694227 is acknowledged. Open access funding provided by Institute of Science and Technology (IST Austria).","article_type":"original","title":"The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy","_id":"14441","publisher":"Springer Nature","volume":404,"month":"11","oa":1,"date_published":"2023-11-01T00:00:00Z","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"isi":1,"corr_author":"1","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","intvolume":"       404","citation":{"apa":"Brooks, M., &#38; Seiringer, R. (2023). The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-023-04841-3\">https://doi.org/10.1007/s00220-023-04841-3</a>","mla":"Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” <i>Communications in Mathematical Physics</i>, vol. 404, Springer Nature, 2023, pp. 287–337, doi:<a href=\"https://doi.org/10.1007/s00220-023-04841-3\">10.1007/s00220-023-04841-3</a>.","ista":"Brooks M, Seiringer R. 2023. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. Communications in Mathematical Physics. 404, 287–337.","chicago":"Brooks, Morris, and Robert Seiringer. “The Fröhlich Polaron at Strong Coupling: Part I - The Quantum Correction to the Classical Energy.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00220-023-04841-3\">https://doi.org/10.1007/s00220-023-04841-3</a>.","ieee":"M. Brooks and R. Seiringer, “The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy,” <i>Communications in Mathematical Physics</i>, vol. 404. Springer Nature, pp. 287–337, 2023.","short":"M. Brooks, R. Seiringer, Communications in Mathematical Physics 404 (2023) 287–337.","ama":"Brooks M, Seiringer R. The Fröhlich Polaron at strong coupling: Part I - The quantum correction to the classical energy. <i>Communications in Mathematical Physics</i>. 2023;404:287-337. doi:<a href=\"https://doi.org/10.1007/s00220-023-04841-3\">10.1007/s00220-023-04841-3</a>"},"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa_version":"Published Version","publication_status":"published","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00220-023-04841-3","date_created":"2023-10-22T22:01:13Z","external_id":{"isi":["001096217400007"],"arxiv":["2207.03156"]},"abstract":[{"text":"We study the Fröhlich polaron model in R3, and establish the subleading term in the strong coupling asymptotics of its ground state energy, corresponding to the quantum corrections to the classical energy determined by the Pekar approximation.","lang":"eng"}],"author":[{"orcid":"0000-0002-6249-0928","id":"B7ECF9FC-AA38-11E9-AC9A-0930E6697425","first_name":"Morris","full_name":"Brooks, Morris","last_name":"Brooks"},{"full_name":"Seiringer, Robert","first_name":"Robert","orcid":"0000-0002-6781-0521","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","last_name":"Seiringer"}],"file_date_updated":"2023-10-31T12:21:39Z"},{"author":[{"last_name":"Schnelli","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","first_name":"Kevin"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","orcid":"0000-0003-1559-1205","full_name":"Xu, Yuanyuan","first_name":"Yuanyuan","last_name":"Xu"}],"abstract":[{"text":"We show that the fluctuations of the largest eigenvalue of a real symmetric or complex Hermitian Wigner matrix of size N converge to the Tracy–Widom laws at a rate O(N^{-1/3+\\omega }), as N tends to infinity. For Wigner matrices this improves the previous rate O(N^{-2/9+\\omega }) obtained by Bourgade (J Eur Math Soc, 2021) for generalized Wigner matrices. Our result follows from a Green function comparison theorem, originally introduced by Erdős et al. (Adv Math 229(3):1435–1515, 2012) to prove edge universality, on a finer spectral parameter scale with improved error estimates. The proof relies on the continuous Green function flow induced by a matrix-valued Ornstein–Uhlenbeck process. Precise estimates on leading contributions from the third and fourth order moments of the matrix entries are obtained using iterative cumulant expansions and recursive comparisons for correlation functions, along with uniform convergence estimates for correlation kernels of the Gaussian invariant ensembles.","lang":"eng"}],"external_id":{"pmid":["35765414"],"arxiv":["2102.04330"],"isi":["000782737200001"]},"file_date_updated":"2022-08-05T06:01:13Z","oa_version":"Published Version","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"article_processing_charge":"No","doi":"10.1007/s00220-022-04377-y","publication_status":"published","date_created":"2022-04-24T22:01:44Z","citation":{"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>","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>.","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>.","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.","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>","short":"K. Schnelli, Y. Xu, Communications in Mathematical Physics 393 (2022) 839–907."},"intvolume":"       393","publication":"Communications in Mathematical Physics","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"language":[{"iso":"eng"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"07","volume":393,"date_published":"2022-07-01T00:00:00Z","oa":1,"_id":"11332","publisher":"Springer Nature","article_type":"original","title":"Convergence rate to the Tracy–Widom laws for the largest Eigenvalue of Wigner matrices","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.","quality_controlled":"1","arxiv":1,"file":[{"file_name":"2022_CommunMathPhys_Schnelli.pdf","relation":"main_file","content_type":"application/pdf","creator":"dernst","date_updated":"2022-08-05T06:01:13Z","file_size":1141462,"checksum":"bee0278c5efa9a33d9a2dc8d354a6c51","date_created":"2022-08-05T06:01:13Z","file_id":"11726","access_level":"open_access","success":1}],"year":"2022","department":[{"_id":"LaEr"}],"type":"journal_article","has_accepted_license":"1","status":"public","ec_funded":1,"page":"839-907","project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","grant_number":"101020331","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"fulldoi":"https://doi.org/10.1007/s00220-022-04377-y","pmid":1,"date_updated":"2025-06-11T14:01:05Z","day":"01","scopus_import":"1","ddc":["510"]},{"volume":389,"month":"02","das_tickbox":"1","date_published":"2022-02-01T00:00:00Z","OA_place":"repository","oa":1,"_id":"22043","publisher":"Springer Nature","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2009.06746"}],"article_type":"original","title":"Orbital stability of KdV multisolitons in H-1","abstract":[{"lang":"eng","text":"We prove that multisoliton solutions of the Korteweg–de Vries equation are orbitally stable in H^-1(R). We introduce a variational characterization of multisolitons that remains meaningful at such low regularity and show that all optimizing sequences converge to the manifold of multisolitons. The proximity required at the initial time is uniform across the entire manifold of multisolitons; this had not been demonstrated previously, even in H^-1."}],"author":[{"last_name":"Killip","first_name":"Rowan","full_name":"Killip, Rowan"},{"full_name":"Visan, Monica","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan"}],"external_id":{"arxiv":["2009.06746"]},"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa_version":"Preprint","article_processing_charge":"No","date_created":"2026-06-19T07:46:39Z","publication_status":"published","doi":"10.1007/s00220-021-04280-y","intvolume":"       389","citation":{"short":"R. Killip, M. Vişan, Communications in Mathematical Physics 389 (2022) 1445–1473.","ama":"Killip R, Vişan M. Orbital stability of KdV multisolitons in H-1. <i>Communications in Mathematical Physics</i>. 2022;389(3):1445-1473. doi:<a href=\"https://doi.org/10.1007/s00220-021-04280-y\">10.1007/s00220-021-04280-y</a>","ieee":"R. Killip and M. Vişan, “Orbital stability of KdV multisolitons in H-1,” <i>Communications in Mathematical Physics</i>, vol. 389, no. 3. Springer Nature, pp. 1445–1473, 2022.","chicago":"Killip, Rowan, and Monica Vişan. “Orbital Stability of KdV Multisolitons in H-1.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2022. <a href=\"https://doi.org/10.1007/s00220-021-04280-y\">https://doi.org/10.1007/s00220-021-04280-y</a>.","ista":"Killip R, Vişan M. 2022. Orbital stability of KdV multisolitons in H-1. Communications in Mathematical Physics. 389(3), 1445–1473.","mla":"Killip, Rowan, and Monica Vişan. “Orbital Stability of KdV Multisolitons in H-1.” <i>Communications in Mathematical Physics</i>, vol. 389, no. 3, Springer Nature, 2022, pp. 1445–73, doi:<a href=\"https://doi.org/10.1007/s00220-021-04280-y\">10.1007/s00220-021-04280-y</a>.","apa":"Killip, R., &#38; Vişan, M. (2022). Orbital stability of KdV multisolitons in H-1. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04280-y\">https://doi.org/10.1007/s00220-021-04280-y</a>"},"publication":"Communications in Mathematical Physics","extern":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"type":"journal_article","status":"public","page":"1445-1473","issue":"3","fulldoi":"https://doi.org/10.1007/s00220-021-04280-y","date_updated":"2026-06-25T07:41:51Z","day":"01","scopus_import":"1","OA_type":"green","quality_controlled":"1","arxiv":1,"year":"2022"},{"department":[{"_id":"LaEr"}],"year":"2021","file":[{"file_size":841426,"date_created":"2022-02-02T10:19:55Z","access_level":"open_access","file_id":"10715","checksum":"a2c7b6f5d23b5453cd70d1261272283b","success":1,"content_type":"application/pdf","relation":"main_file","file_name":"2021_CommunMathPhys_Cipolloni.pdf","creator":"cchlebak","date_updated":"2022-02-02T10:19:55Z"}],"arxiv":1,"quality_controlled":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","ddc":["510"],"scopus_import":"1","day":"29","date_updated":"2025-04-15T06:53:08Z","fulldoi":"https://doi.org/10.1007/s00220-021-04239-z","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"page":"1005–1048","issue":"2","status":"public","has_accepted_license":"1","type":"journal_article","language":[{"iso":"eng"}],"isi":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","corr_author":"1","publication":"Communications in Mathematical Physics","intvolume":"       388","citation":{"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>.","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>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","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>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <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>.","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."},"publication_status":"published","date_created":"2021-11-07T23:01:25Z","article_processing_charge":"Yes (via OA deal)","doi":"10.1007/s00220-021-04239-z","oa_version":"Published Version","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"file_date_updated":"2022-02-02T10:19:55Z","external_id":{"isi":["000712232700001"],"arxiv":["2012.13215"]},"author":[{"full_name":"Cipolloni, Giorgio","first_name":"Giorgio","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni"},{"first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"}],"abstract":[{"text":"We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).","lang":"eng"}],"title":"Eigenstate thermalization hypothesis for Wigner matrices","article_type":"original","publisher":"Springer Nature","_id":"10221","oa":1,"date_published":"2021-10-29T00:00:00Z","month":"10","volume":388,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}},{"status":"public","has_accepted_license":"1","type":"journal_article","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"page":"83–117","issue":"1","date_updated":"2025-07-10T12:01:25Z","day":"01","fulldoi":"https://doi.org/10.1007/s00220-020-03902-1","ddc":["510"],"scopus_import":"1","acknowledgement":"The authors thank Yuki Arano, Nils Carqueville, Alexei Davydov, Reiner Lauterbach, Pau Enrique Moliner, Chris Heunen, André Henriques, Ehud Meir, Catherine Meusburger, Gregor Schaumann, Richard Szabo and Stefan Wagner for helpful discussions and comments. We also thank the referees for their detailed comments which significantly improved the exposition of this paper. LS is supported by the DFG Research Training Group 1670 “Mathematics Inspired by String Theory and Quantum Field Theory”. Open access funding provided by Institute of Science and Technology (IST Austria).","quality_controlled":"1","department":[{"_id":"MiLe"}],"year":"2021","file":[{"file_name":"2021_CommMathPhys_Runkel.pdf","relation":"main_file","content_type":"application/pdf","creator":"dernst","date_updated":"2021-02-03T15:00:30Z","file_size":790526,"checksum":"6f451f9c2b74bedbc30cf884a3e02670","access_level":"open_access","date_created":"2021-02-03T15:00:30Z","file_id":"9081","success":1}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"oa":1,"date_published":"2021-01-01T00:00:00Z","month":"01","volume":381,"publisher":"Springer Nature","_id":"8816","title":"Area-dependent quantum field theory","article_type":"original","file_date_updated":"2021-02-03T15:00:30Z","external_id":{"isi":["000591139000001"]},"abstract":[{"lang":"eng","text":"Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail."}],"author":[{"first_name":"Ingo","full_name":"Runkel, Ingo","last_name":"Runkel"},{"first_name":"Lorant","full_name":"Szegedy, Lorant","orcid":"0000-0003-2834-5054","id":"7943226E-220E-11EA-94C7-D59F3DDC885E","last_name":"Szegedy"}],"publication_status":"published","date_created":"2020-11-29T23:01:17Z","doi":"10.1007/s00220-020-03902-1","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"publication":"Communications in Mathematical Physics","citation":{"mla":"Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.” <i>Communications in Mathematical Physics</i>, vol. 381, no. 1, Springer Nature, 2021, pp. 83–117, doi:<a href=\"https://doi.org/10.1007/s00220-020-03902-1\">10.1007/s00220-020-03902-1</a>.","apa":"Runkel, I., &#38; Szegedy, L. (2021). Area-dependent quantum field theory. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-020-03902-1\">https://doi.org/10.1007/s00220-020-03902-1</a>","ieee":"I. Runkel and L. Szegedy, “Area-dependent quantum field theory,” <i>Communications in Mathematical Physics</i>, vol. 381, no. 1. Springer Nature, pp. 83–117, 2021.","ista":"Runkel I, Szegedy L. 2021. Area-dependent quantum field theory. Communications in Mathematical Physics. 381(1), 83–117.","chicago":"Runkel, Ingo, and Lorant Szegedy. “Area-Dependent Quantum Field Theory.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-020-03902-1\">https://doi.org/10.1007/s00220-020-03902-1</a>.","ama":"Runkel I, Szegedy L. Area-dependent quantum field theory. <i>Communications in Mathematical Physics</i>. 2021;381(1):83–117. doi:<a href=\"https://doi.org/10.1007/s00220-020-03902-1\">10.1007/s00220-020-03902-1</a>","short":"I. Runkel, L. Szegedy, Communications in Mathematical Physics 381 (2021) 83–117."},"intvolume":"       381","language":[{"iso":"eng"}],"isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"corr_author":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","isi":1,"language":[{"iso":"eng"}],"citation":{"chicago":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>.","ista":"Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups. Communications in Mathematical Physics. 387, 761–791.","ieee":"M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,” <i>Communications in Mathematical Physics</i>, vol. 387. Springer Nature, pp. 761–791, 2021.","short":"M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.","ama":"Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. 2021;387:761–791. doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>","mla":"Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum Markov Semigroups.” <i>Communications in Mathematical Physics</i>, vol. 387, Springer Nature, 2021, pp. 761–791, doi:<a href=\"https://doi.org/10.1007/s00220-021-04199-4\">10.1007/s00220-021-04199-4</a>.","apa":"Wirth, M., &#38; Zhang, H. (2021). Complete gradient estimates of quantum Markov semigroups. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04199-4\">https://doi.org/10.1007/s00220-021-04199-4</a>"},"intvolume":"       387","publication":"Communications in Mathematical Physics","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa_version":"Published Version","date_created":"2021-08-30T10:07:44Z","publication_status":"published","doi":"10.1007/s00220-021-04199-4","article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Wirth","first_name":"Melchior","full_name":"Wirth, Melchior","orcid":"0000-0002-0519-4241","id":"88644358-0A0E-11EA-8FA5-49A33DDC885E"},{"last_name":"Zhang","id":"D8F41E38-9E66-11E9-A9E2-65C2E5697425","first_name":"Haonan","full_name":"Zhang, Haonan"}],"abstract":[{"text":"In this article we introduce a complete gradient estimate for symmetric quantum Markov semigroups on von Neumann algebras equipped with a normal faithful tracial state, which implies semi-convexity of the entropy with respect to the recently introduced noncommutative 2-Wasserstein distance. We show that this complete gradient estimate is stable under tensor products and free products and establish its validity for a number of examples. As an application we prove a complete modified logarithmic Sobolev inequality with optimal constant for Poisson-type semigroups on free group factors.","lang":"eng"}],"external_id":{"isi":["000691214200001"],"pmid":["34776525"],"arxiv":["2007.13506"]},"file_date_updated":"2021-09-08T09:46:34Z","article_type":"original","title":"Complete gradient estimates of quantum Markov semigroups","_id":"9973","publisher":"Springer Nature","month":"08","volume":387,"date_published":"2021-08-30T00:00:00Z","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"file":[{"file_id":"9990","access_level":"open_access","date_created":"2021-09-08T07:34:24Z","checksum":"8a602f916b1c2b0dc1159708b7cb204b","file_size":505971,"date_updated":"2021-09-08T09:46:34Z","creator":"cchlebak","content_type":"application/pdf","relation":"main_file","file_name":"2021_CommunMathPhys_Wirth.pdf"}],"year":"2021","department":[{"_id":"JaMa"}],"arxiv":1,"keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"quality_controlled":"1","acknowledgement":"Both authors would like to thank Jan Maas for fruitful discussions and helpful comments.","scopus_import":"1","ddc":["621"],"pmid":1,"fulldoi":"https://doi.org/10.1007/s00220-021-04199-4","date_updated":"2025-06-12T06:30:13Z","day":"30","page":"761–791","ec_funded":1,"project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"},{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"},{"grant_number":"F6504","name":"Taming Complexity in Partial Differential Systems","_id":"fc31cba2-9c52-11eb-aca3-ff467d239cd2"}],"type":"journal_article","has_accepted_license":"1","status":"public"},{"type":"journal_article","status":"public","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","name":"International IST Postdoc Fellowship Programme","grant_number":"291734","call_identifier":"FP7"}],"issue":"9","page":"1649-1675","ec_funded":1,"date_updated":"2025-07-10T11:57:03Z","day":"01","fulldoi":"https://doi.org/10.1007/s00220-020-03828-8","scopus_import":"1","acknowledgement":"We thank Andrea Sportiello for sharing his insights on perturbative regimes of the Abelian sandpile model which was the starting point of our work. We also thank Grigory Mikhalkin, who encouraged us to approach this problem. We thank an anonymous referee. Also we thank Misha Khristoforov and Sergey Lanzat who participated on the initial state of this project, when we had nothing except the computer simulation and pictures. We thank Mikhail Raskin for providing us the code on Golly for faster simulations. Ilia Zharkov, Ilia Itenberg, Kristin Shaw, Max Karev, Lionel Levine, Ernesto Lupercio, Pavol Ševera, Yulieth Prieto, Michael Polyak, Danila Cherkashin asked us a lot of questions and listened to us; not all of their questions found answers here, but we are going to treat them in subsequent papers.","quality_controlled":"1","arxiv":1,"year":"2020","department":[{"_id":"TaHa"}],"month":"09","volume":378,"oa":1,"date_published":"2020-09-01T00:00:00Z","_id":"8325","publisher":"Springer Nature","article_type":"original","main_file_link":[{"url":"https://arxiv.org/abs/1711.04285","open_access":"1"}],"title":"Sandpile solitons via smoothing of superharmonic functions","external_id":{"arxiv":["1711.04285"],"isi":["000560620600001"]},"abstract":[{"lang":"eng","text":"Let 𝐹:ℤ2→ℤ be the pointwise minimum of several linear functions. The theory of smoothing allows us to prove that under certain conditions there exists the pointwise minimal function among all integer-valued superharmonic functions coinciding with F “at infinity”. We develop such a theory to prove existence of so-called solitons (or strings) in a sandpile model, studied by S. Caracciolo, G. Paoletti, and A. Sportiello. Thus we made a step towards understanding the phenomena of the identity in the sandpile group for planar domains where solitons appear according to experiments. We prove that sandpile states, defined using our smoothing procedure, move changeless when we apply the wave operator (that is why we call them solitons), and can interact, forming triads and nodes. "}],"author":[{"first_name":"Nikita","full_name":"Kalinin, Nikita","last_name":"Kalinin"},{"last_name":"Shkolnikov","full_name":"Shkolnikov, Mikhail","first_name":"Mikhail","id":"35084A62-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4310-178X"}],"publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa_version":"Preprint","article_processing_charge":"No","publication_status":"published","doi":"10.1007/s00220-020-03828-8","date_created":"2020-08-30T22:01:13Z","publication":"Communications in Mathematical Physics","intvolume":"       378","citation":{"mla":"Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of Superharmonic Functions.” <i>Communications in Mathematical Physics</i>, vol. 378, no. 9, Springer Nature, 2020, pp. 1649–75, doi:<a href=\"https://doi.org/10.1007/s00220-020-03828-8\">10.1007/s00220-020-03828-8</a>.","apa":"Kalinin, N., &#38; Shkolnikov, M. (2020). Sandpile solitons via smoothing of superharmonic functions. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-020-03828-8\">https://doi.org/10.1007/s00220-020-03828-8</a>","ista":"Kalinin N, Shkolnikov M. 2020. Sandpile solitons via smoothing of superharmonic functions. Communications in Mathematical Physics. 378(9), 1649–1675.","chicago":"Kalinin, Nikita, and Mikhail Shkolnikov. “Sandpile Solitons via Smoothing of Superharmonic Functions.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-020-03828-8\">https://doi.org/10.1007/s00220-020-03828-8</a>.","ieee":"N. Kalinin and M. Shkolnikov, “Sandpile solitons via smoothing of superharmonic functions,” <i>Communications in Mathematical Physics</i>, vol. 378, no. 9. Springer Nature, pp. 1649–1675, 2020.","ama":"Kalinin N, Shkolnikov M. Sandpile solitons via smoothing of superharmonic functions. <i>Communications in Mathematical Physics</i>. 2020;378(9):1649-1675. doi:<a href=\"https://doi.org/10.1007/s00220-020-03828-8\">10.1007/s00220-020-03828-8</a>","short":"N. Kalinin, M. Shkolnikov, Communications in Mathematical Physics 378 (2020) 1649–1675."},"isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}]},{"department":[{"_id":"RoSe"}],"file":[{"file_size":853289,"checksum":"f9dd6dd615a698f1d3636c4a092fed23","access_level":"open_access","date_created":"2019-07-24T07:19:10Z","file_id":"6668","relation":"main_file","file_name":"2019_CommMathPhysics_Benedikter.pdf","content_type":"application/pdf","creator":"dernst","date_updated":"2020-07-14T12:47:35Z"}],"year":"2020","arxiv":1,"quality_controlled":"1","ddc":["530"],"scopus_import":"1","fulldoi":"https://doi.org/10.1007/s00220-019-03505-5","date_updated":"2025-04-14T07:27:00Z","day":"01","page":"2097–2150","ec_funded":1,"project":[{"_id":"3AC91DDA-15DF-11EA-824D-93A3E7B544D1","name":"FWF Open Access Fund","call_identifier":"FWF"},{"_id":"25C878CE-B435-11E9-9278-68D0E5697425","call_identifier":"FWF","name":"Structure of the Excitation Spectrum for Many-Body Quantum Systems","grant_number":"P27533_N27"},{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"has_accepted_license":"1","status":"public","type":"journal_article","language":[{"iso":"eng"}],"corr_author":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"intvolume":"       374","citation":{"mla":"Benedikter, Niels P., et al. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>, vol. 374, Springer Nature, 2020, pp. 2097–2150, doi:<a href=\"https://doi.org/10.1007/s00220-019-03505-5\">10.1007/s00220-019-03505-5</a>.","apa":"Benedikter, N. P., Nam, P. T., Porta, M., Schlein, B., &#38; Seiringer, R. (2020). Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03505-5\">https://doi.org/10.1007/s00220-019-03505-5</a>","ama":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. <i>Communications in Mathematical Physics</i>. 2020;374:2097–2150. doi:<a href=\"https://doi.org/10.1007/s00220-019-03505-5\">10.1007/s00220-019-03505-5</a>","short":"N.P. Benedikter, P.T. Nam, M. Porta, B. Schlein, R. Seiringer, Communications in Mathematical Physics 374 (2020) 2097–2150.","chicago":"Benedikter, Niels P, Phan Thành Nam, Marcello Porta, Benjamin Schlein, and Robert Seiringer. “Optimal Upper Bound for the Correlation Energy of a Fermi Gas in the Mean-Field Regime.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03505-5\">https://doi.org/10.1007/s00220-019-03505-5</a>.","ista":"Benedikter NP, Nam PT, Porta M, Schlein B, Seiringer R. 2020. Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime. Communications in Mathematical Physics. 374, 2097–2150.","ieee":"N. P. Benedikter, P. T. Nam, M. Porta, B. Schlein, and R. Seiringer, “Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime,” <i>Communications in Mathematical Physics</i>, vol. 374. Springer Nature, pp. 2097–2150, 2020."},"publication":"Communications in Mathematical Physics","date_created":"2019-07-18T13:30:04Z","doi":"10.1007/s00220-019-03505-5","publication_status":"published","article_processing_charge":"No","oa_version":"Published Version","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"file_date_updated":"2020-07-14T12:47:35Z","abstract":[{"text":"While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.\r\n","lang":"eng"}],"author":[{"first_name":"Niels P","full_name":"Benedikter, Niels P","orcid":"0000-0002-1071-6091","id":"3DE6C32A-F248-11E8-B48F-1D18A9856A87","last_name":"Benedikter"},{"first_name":"Phan Thành","full_name":"Nam, Phan Thành","last_name":"Nam"},{"first_name":"Marcello","full_name":"Porta, Marcello","last_name":"Porta"},{"last_name":"Schlein","first_name":"Benjamin","full_name":"Schlein, Benjamin"},{"last_name":"Seiringer","first_name":"Robert","full_name":"Seiringer, Robert","id":"4AFD0470-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-6781-0521"}],"external_id":{"arxiv":["1809.01902"],"isi":["000527910700019"]},"title":"Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime","article_type":"original","publisher":"Springer Nature","_id":"6649","date_published":"2020-03-01T00:00:00Z","oa":1,"volume":374,"month":"03","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"}},{"project":[{"_id":"25C6DC12-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Analysis of quantum many-body systems","grant_number":"694227"}],"ec_funded":1,"page":"1311-1395","type":"journal_article","status":"public","scopus_import":"1","day":"01","date_updated":"2025-04-14T07:27:00Z","fulldoi":"https://doi.org/10.1007/s00220-019-03555-9","quality_controlled":"1","acknowledgement":"We would like to thank P. T. Nam and R. Seiringer for several useful discussions and\r\nfor suggesting us to use the localization techniques from [9]. C. Boccato has received funding from the\r\nEuropean Research Council (ERC) under the programme Horizon 2020 (Grant Agreement 694227). B. Schlein gratefully acknowledges support from the NCCR SwissMAP and from the Swiss National Foundation of Science (Grant No. 200020_1726230) through the SNF Grant “Dynamical and energetic properties of Bose–Einstein condensates”.","year":"2020","department":[{"_id":"RoSe"}],"arxiv":1,"volume":376,"month":"06","oa":1,"date_published":"2020-06-01T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/1812.03086","open_access":"1"}],"article_type":"original","title":"Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime","_id":"6906","publisher":"Springer","oa_version":"Preprint","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"doi":"10.1007/s00220-019-03555-9","publication_status":"published","date_created":"2019-09-24T17:30:59Z","article_processing_charge":"No","external_id":{"arxiv":["1812.03086"],"isi":["000536053300012"]},"author":[{"last_name":"Boccato","first_name":"Chiara","full_name":"Boccato, Chiara","id":"342E7E22-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Christian","full_name":"Brennecke, Christian","last_name":"Brennecke"},{"last_name":"Cenatiempo","full_name":"Cenatiempo, Serena","first_name":"Serena"},{"full_name":"Schlein, Benjamin","first_name":"Benjamin","last_name":"Schlein"}],"abstract":[{"text":"We consider systems of bosons trapped in a box, in the Gross–Pitaevskii regime. We show that low-energy states exhibit complete Bose–Einstein condensation with an optimal bound on the number of orthogonal excitations. This extends recent results obtained in Boccato et al. (Commun Math Phys 359(3):975–1026, 2018), removing the assumption of small interaction potential.","lang":"eng"}],"isi":1,"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","language":[{"iso":"eng"}],"publication":"Communications in Mathematical Physics","citation":{"mla":"Boccato, Chiara, et al. “Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.” <i>Communications in Mathematical Physics</i>, vol. 376, Springer, 2020, pp. 1311–95, doi:<a href=\"https://doi.org/10.1007/s00220-019-03555-9\">10.1007/s00220-019-03555-9</a>.","apa":"Boccato, C., Brennecke, C., Cenatiempo, S., &#38; Schlein, B. (2020). Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. <i>Communications in Mathematical Physics</i>. Springer. <a href=\"https://doi.org/10.1007/s00220-019-03555-9\">https://doi.org/10.1007/s00220-019-03555-9</a>","ama":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. <i>Communications in Mathematical Physics</i>. 2020;376:1311-1395. doi:<a href=\"https://doi.org/10.1007/s00220-019-03555-9\">10.1007/s00220-019-03555-9</a>","short":"C. Boccato, C. Brennecke, S. Cenatiempo, B. Schlein, Communications in Mathematical Physics 376 (2020) 1311–1395.","ista":"Boccato C, Brennecke C, Cenatiempo S, Schlein B. 2020. Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime. Communications in Mathematical Physics. 376, 1311–1395.","ieee":"C. Boccato, C. Brennecke, S. Cenatiempo, and B. Schlein, “Optimal rate for Bose-Einstein condensation in the Gross-Pitaevskii regime,” <i>Communications in Mathematical Physics</i>, vol. 376. Springer, pp. 1311–1395, 2020.","chicago":"Boccato, Chiara, Christian Brennecke, Serena Cenatiempo, and Benjamin Schlein. “Optimal Rate for Bose-Einstein Condensation in the Gross-Pitaevskii Regime.” <i>Communications in Mathematical Physics</i>. Springer, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03555-9\">https://doi.org/10.1007/s00220-019-03555-9</a>."},"intvolume":"       376"},{"year":"2020","department":[{"_id":"TaHa"}],"arxiv":1,"quality_controlled":"1","scopus_import":"1","fulldoi":"https://doi.org/10.1007/s00220-019-03575-5","date_updated":"2025-04-14T09:12:46Z","day":"01","page":"1803-1873","ec_funded":1,"project":[{"call_identifier":"FP7","grant_number":"320593","name":"Arithmetic and physics of Higgs moduli spaces","_id":"25E549F4-B435-11E9-9278-68D0E5697425"}],"type":"journal_article","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"language":[{"iso":"eng"}],"intvolume":"       376","citation":{"short":"M. Rapcak, Y. Soibelman, Y. Yang, G. Zhao, Communications in Mathematical Physics 376 (2020) 1803–1873.","ama":"Rapcak M, Soibelman Y, Yang Y, Zhao G. Cohomological Hall algebras, vertex algebras and instantons. <i>Communications in Mathematical Physics</i>. 2020;376:1803-1873. doi:<a href=\"https://doi.org/10.1007/s00220-019-03575-5\">10.1007/s00220-019-03575-5</a>","ista":"Rapcak M, Soibelman Y, Yang Y, Zhao G. 2020. Cohomological Hall algebras, vertex algebras and instantons. Communications in Mathematical Physics. 376, 1803–1873.","ieee":"M. Rapcak, Y. Soibelman, Y. Yang, and G. Zhao, “Cohomological Hall algebras, vertex algebras and instantons,” <i>Communications in Mathematical Physics</i>, vol. 376. Springer Nature, pp. 1803–1873, 2020.","chicago":"Rapcak, Miroslav, Yan Soibelman, Yaping Yang, and Gufang Zhao. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03575-5\">https://doi.org/10.1007/s00220-019-03575-5</a>.","mla":"Rapcak, Miroslav, et al. “Cohomological Hall Algebras, Vertex Algebras and Instantons.” <i>Communications in Mathematical Physics</i>, vol. 376, Springer Nature, 2020, pp. 1803–73, doi:<a href=\"https://doi.org/10.1007/s00220-019-03575-5\">10.1007/s00220-019-03575-5</a>.","apa":"Rapcak, M., Soibelman, Y., Yang, Y., &#38; Zhao, G. (2020). Cohomological Hall algebras, vertex algebras and instantons. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03575-5\">https://doi.org/10.1007/s00220-019-03575-5</a>"},"publication":"Communications in Mathematical Physics","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa_version":"Preprint","article_processing_charge":"No","publication_status":"published","date_created":"2019-11-12T14:01:27Z","doi":"10.1007/s00220-019-03575-5","abstract":[{"lang":"eng","text":"We define an action of the (double of) Cohomological Hall algebra of Kontsevich and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We identify this action with the one of the affine Yangian of gl(1). Based on that we derive the vertex algebra at the corner Wr1,r2,r3 of Gaiotto and Rapčák. We conjecture that our approach works for a big class of Calabi–Yau categories, including those associated with toric Calabi–Yau 3-folds."}],"author":[{"first_name":"Miroslav","full_name":"Rapcak, Miroslav","last_name":"Rapcak"},{"last_name":"Soibelman","full_name":"Soibelman, Yan","first_name":"Yan"},{"full_name":"Yang, Yaping","first_name":"Yaping","last_name":"Yang"},{"id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","first_name":"Gufang","full_name":"Zhao, Gufang","last_name":"Zhao"}],"external_id":{"isi":["000536255500004"],"arxiv":["1810.10402"]},"article_type":"original","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1810.10402"}],"title":"Cohomological Hall algebras, vertex algebras and instantons","_id":"7004","publisher":"Springer Nature","volume":376,"month":"06","date_published":"2020-06-01T00:00:00Z","oa":1},{"_id":"6185","publisher":"Springer Nature","article_type":"original","title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"month":"09","volume":378,"date_published":"2020-09-01T00:00:00Z","oa":1,"intvolume":"       378","citation":{"ama":"Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I: Local law and the complex Hermitian case. <i>Communications in Mathematical Physics</i>. 2020;378:1203-1278. doi:<a href=\"https://doi.org/10.1007/s00220-019-03657-4\">10.1007/s00220-019-03657-4</a>","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03657-4\">https://doi.org/10.1007/s00220-019-03657-4</a>.","ista":"Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 378, 1203–1278.","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” <i>Communications in Mathematical Physics</i>, vol. 378. Springer Nature, pp. 1203–1278, 2020.","mla":"Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” <i>Communications in Mathematical Physics</i>, vol. 378, Springer Nature, 2020, pp. 1203–78, doi:<a href=\"https://doi.org/10.1007/s00220-019-03657-4\">10.1007/s00220-019-03657-4</a>.","apa":"Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2020). Cusp universality for random matrices I: Local law and the complex Hermitian case. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03657-4\">https://doi.org/10.1007/s00220-019-03657-4</a>"},"publication":"Communications in Mathematical Physics","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"related_material":{"record":[{"id":"6179","status":"public","relation":"dissertation_contains"}]},"language":[{"iso":"eng"}],"author":[{"last_name":"Erdös","full_name":"Erdös, László","first_name":"László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger"},{"first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder"}],"abstract":[{"lang":"eng","text":"For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969)."}],"external_id":{"arxiv":["1809.03971"],"isi":["000529483000001"]},"file_date_updated":"2020-11-18T11:14:37Z","publication_identifier":{"issn":["0010-3616"],"eissn":["1432-0916"]},"oa_version":"Published Version","doi":"10.1007/s00220-019-03657-4","article_processing_charge":"Yes (via OA deal)","date_created":"2019-03-28T10:21:15Z","publication_status":"published","fulldoi":"https://doi.org/10.1007/s00220-019-03657-4","day":"01","date_updated":"2026-07-29T13:46:19Z","scopus_import":"1","ddc":["530","510"],"type":"journal_article","has_accepted_license":"1","status":"public","page":"1203-1278","ec_funded":1,"project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"arxiv":1,"file":[{"date_updated":"2020-11-18T11:14:37Z","creator":"dernst","relation":"main_file","file_name":"2020_CommMathPhysics_Erdoes.pdf","content_type":"application/pdf","success":1,"checksum":"c3a683e2afdcea27afa6880b01e53dc2","file_id":"8771","date_created":"2020-11-18T11:14:37Z","access_level":"open_access","file_size":2904574}],"year":"2020","department":[{"_id":"LaEr"}],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to Johannes Alt for numerous discussions on the Dyson equation and for his invaluable help in adjusting [10] to the needs of the present work.","quality_controlled":"1"},{"acknowledgement":"OA fund by IST Austria","quality_controlled":"1","OA_type":"hybrid","department":[{"_id":"RoSe"}],"year":"2019","file":[{"checksum":"cd283b475dd739e04655315abd46f528","file_id":"7101","date_created":"2019-11-25T08:11:11Z","access_level":"open_access","file_size":884469,"date_updated":"2020-07-14T12:47:49Z","creator":"dernst","file_name":"2019_CommMathPhys_Jeblick.pdf","relation":"main_file","content_type":"application/pdf"}],"status":"public","has_accepted_license":"1","type":"journal_article","project":[{"call_identifier":"H2020","grant_number":"694227","name":"Analysis of quantum many-body systems","_id":"25C6DC12-B435-11E9-9278-68D0E5697425"}],"ec_funded":1,"issue":"1","page":"1-69","day":"08","date_updated":"2026-07-28T13:04:54Z","fulldoi":"https://doi.org/10.1007/s00220-019-03599-x","ddc":["510"],"scopus_import":"1","file_date_updated":"2020-07-14T12:47:49Z","external_id":{"isi":["000495193700002"]},"author":[{"last_name":"Jeblick","first_name":"Maximilian","full_name":"Jeblick, Maximilian"},{"id":"4BC40BEC-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-0495-6822","full_name":"Leopold, Nikolai K","first_name":"Nikolai K","last_name":"Leopold"},{"last_name":"Pickl","full_name":"Pickl, Peter","first_name":"Peter"}],"abstract":[{"text":"We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman interacting N-particle system of bosons. We consider the interaction potential to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx), for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrödinger equation in trace norm. For the latter potential VN we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics.","lang":"eng"}],"date_created":"2019-11-25T08:08:02Z","article_processing_charge":"Yes (via OA deal)","publication_status":"published","doi":"10.1007/s00220-019-03599-x","oa_version":"Published Version","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"publication":"Communications in Mathematical Physics","intvolume":"       372","citation":{"apa":"Jeblick, M., Leopold, N. K., &#38; Pickl, P. (2019). Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03599-x\">https://doi.org/10.1007/s00220-019-03599-x</a>","mla":"Jeblick, Maximilian, et al. “Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” <i>Communications in Mathematical Physics</i>, vol. 372, no. 1, Springer Nature, 2019, pp. 1–69, doi:<a href=\"https://doi.org/10.1007/s00220-019-03599-x\">10.1007/s00220-019-03599-x</a>.","ieee":"M. Jeblick, N. K. Leopold, and P. Pickl, “Derivation of the time dependent Gross–Pitaevskii equation in two dimensions,” <i>Communications in Mathematical Physics</i>, vol. 372, no. 1. Springer Nature, pp. 1–69, 2019.","chicago":"Jeblick, Maximilian, Nikolai K Leopold, and Peter Pickl. “Derivation of the Time Dependent Gross–Pitaevskii Equation in Two Dimensions.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2019. <a href=\"https://doi.org/10.1007/s00220-019-03599-x\">https://doi.org/10.1007/s00220-019-03599-x</a>.","ista":"Jeblick M, Leopold NK, Pickl P. 2019. Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. Communications in Mathematical Physics. 372(1), 1–69.","ama":"Jeblick M, Leopold NK, Pickl P. Derivation of the time dependent Gross–Pitaevskii equation in two dimensions. <i>Communications in Mathematical Physics</i>. 2019;372(1):1-69. doi:<a href=\"https://doi.org/10.1007/s00220-019-03599-x\">10.1007/s00220-019-03599-x</a>","short":"M. Jeblick, N.K. Leopold, P. Pickl, Communications in Mathematical Physics 372 (2019) 1–69."},"language":[{"iso":"eng"}],"isi":1,"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","corr_author":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"oa":1,"date_published":"2019-11-08T00:00:00Z","OA_place":"publisher","volume":372,"month":"11","publisher":"Springer Nature","_id":"7100","title":"Derivation of the time dependent Gross–Pitaevskii equation in two dimensions","article_type":"original"}]