[{"title":"On adiabatic theory for extended fermionic lattice systems","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","isi":1,"file":[{"content_type":"application/pdf","access_level":"open_access","success":1,"file_name":"2022_JourMathPhysics_Henheik2.pdf","file_id":"12410","creator":"dernst","date_updated":"2023-01-27T07:10:52Z","relation":"main_file","file_size":5251092,"date_created":"2023-01-27T07:10:52Z","checksum":"213b93750080460718c050e4967cfdb4"}],"_id":"12184","quality_controlled":"1","acknowledgement":"It is a pleasure to thank Stefan Teufel for numerous interesting discussions, fruitful collaboration, and many helpful comments on an earlier version of the manuscript. J.H. acknowledges partial financial support from the ERC Advanced Grant No. 101020331 “Random\r\nmatrices beyond Wigner-Dyson-Mehta.” T.W. acknowledges financial support from the DFG research unit FOR 5413 “Long-range interacting quantum spin systems out of equilibrium: Experiment, Theory and Mathematics.\" ","date_updated":"2023-08-04T09:14:57Z","external_id":{"isi":["000905776200001"],"arxiv":["2208.12220"]},"date_created":"2023-01-15T23:00:52Z","publisher":"AIP Publishing","issue":"12","oa":1,"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d"}],"ec_funded":1,"ddc":["510"],"abstract":[{"text":"We review recent results on adiabatic theory for ground states of extended gapped fermionic lattice systems under several different assumptions. More precisely, we present generalized super-adiabatic theorems for extended but finite and infinite systems, assuming either a uniform gap or a gap in the bulk above the unperturbed ground state. The goal of this Review is to provide an overview of these adiabatic theorems and briefly outline the main ideas and techniques required in their proofs.","lang":"eng"}],"publication_identifier":{"issn":["0022-2488"]},"article_number":"121101","author":[{"last_name":"Henheik","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha"},{"last_name":"Wessel","full_name":"Wessel, Tom","first_name":"Tom"}],"volume":63,"department":[{"_id":"LaEr"}],"status":"public","year":"2022","day":"01","language":[{"iso":"eng"}],"article_type":"original","has_accepted_license":"1","citation":{"ieee":"S. J. Henheik and T. Wessel, “On adiabatic theory for extended fermionic lattice systems,” Journal of Mathematical Physics, vol. 63, no. 12. AIP Publishing, 2022.","mla":"Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” Journal of Mathematical Physics, vol. 63, no. 12, 121101, AIP Publishing, 2022, doi:10.1063/5.0123441.","ista":"Henheik SJ, Wessel T. 2022. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 63(12), 121101.","chicago":"Henheik, Sven Joscha, and Tom Wessel. “On Adiabatic Theory for Extended Fermionic Lattice Systems.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0123441.","ama":"Henheik SJ, Wessel T. On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. 2022;63(12). doi:10.1063/5.0123441","apa":"Henheik, S. J., & Wessel, T. (2022). On adiabatic theory for extended fermionic lattice systems. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0123441","short":"S.J. Henheik, T. Wessel, Journal of Mathematical Physics 63 (2022)."},"publication":"Journal of Mathematical Physics","date_published":"2022-12-01T00:00:00Z","oa_version":"Published Version","scopus_import":"1","file_date_updated":"2023-01-27T07:10:52Z","intvolume":" 63","month":"12","publication_status":"published","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"type":"journal_article","doi":"10.1063/5.0123441","article_processing_charge":"No"},{"external_id":{"isi":["000854878500001"],"arxiv":["2102.02037"]},"date_updated":"2023-08-04T09:24:17Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2102.02037","open_access":"1"}],"acknowledgement":"Geher was supported by the Leverhulme Trust Early Career Fellowship (ECF-2018-125), and also by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. K115383 and K134944).\r\nTitkos was supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grant no. PD128374, grant no. K115383 and K134944), by the J´anos Bolyai Research Scholarship of the Hungarian Academy of Sciences, and by the UNKP-20-5-BGE-1 New National Excellence Program of the ´Ministry of Innovation and Technology.\r\nVirosztek was supported by the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, by the Momentum program of the Hungarian Academy of Sciences under grant agreement no. LP2021-15/2021, and partially supported by the Hungarian National Research, Development and Innovation Office - NKFIH (grants no. K124152 and no. KH129601). ","publisher":"Wiley","date_created":"2023-01-16T09:46:13Z","project":[{"name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"oa":1,"issue":"4","publication_identifier":{"issn":["0024-6107"],"eissn":["1469-7750"]},"abstract":[{"text":"Motivated by Kloeckner’s result on the isometry group of the quadratic Wasserstein space W2(Rn), we describe the isometry group Isom(Wp(E)) for all parameters 0 < p < ∞ and for all separable real Hilbert spaces E. In particular, we show that Wp(X) is isometrically rigid for all Polish space X whenever 0 < p < 1. This is a consequence of our more general result: we prove that W1(X) is isometrically rigid if X is a complete separable metric space that satisfies the strict triangle inequality. Furthermore, we show that this latter rigidity result does not generalise to parameters p > 1, by solving Kloeckner’s problem affirmatively on the existence of mass-splitting isometries. ","lang":"eng"}],"ec_funded":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"The isometry group of Wasserstein spaces: The Hilbertian case","isi":1,"_id":"12214","keyword":["General Mathematics"],"quality_controlled":"1","intvolume":" 106","month":"09","oa_version":"Preprint","scopus_import":"1","date_published":"2022-09-18T00:00:00Z","publication":"Journal of the London Mathematical Society","citation":{"ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “The isometry group of Wasserstein spaces: The Hilbertian case,” Journal of the London Mathematical Society, vol. 106, no. 4. Wiley, pp. 3865–3894, 2022.","mla":"Gehér, György Pál, et al. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical Society, vol. 106, no. 4, Wiley, 2022, pp. 3865–94, doi:10.1112/jlms.12676.","ista":"Gehér GP, Titkos T, Virosztek D. 2022. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 106(4), 3865–3894.","apa":"Gehér, G. P., Titkos, T., & Virosztek, D. (2022). The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. Wiley. https://doi.org/10.1112/jlms.12676","ama":"Gehér GP, Titkos T, Virosztek D. The isometry group of Wasserstein spaces: The Hilbertian case. Journal of the London Mathematical Society. 2022;106(4):3865-3894. doi:10.1112/jlms.12676","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of the London Mathematical Society 106 (2022) 3865–3894.","chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “The Isometry Group of Wasserstein Spaces: The Hilbertian Case.” Journal of the London Mathematical Society. Wiley, 2022. https://doi.org/10.1112/jlms.12676."},"page":"3865-3894","publication_status":"published","article_processing_charge":"No","doi":"10.1112/jlms.12676","type":"journal_article","author":[{"last_name":"Gehér","first_name":"György Pál","full_name":"Gehér, György Pál"},{"first_name":"Tamás","full_name":"Titkos, Tamás","last_name":"Titkos"},{"full_name":"Virosztek, Daniel","first_name":"Daniel","orcid":"0000-0003-1109-5511","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"department":[{"_id":"LaEr"}],"volume":106,"language":[{"iso":"eng"}],"year":"2022","day":"18","status":"public","article_type":"original"},{"volume":23,"department":[{"_id":"LaEr"}],"author":[{"orcid":"0000-0002-4901-7992","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni"},{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"article_type":"original","has_accepted_license":"1","language":[{"iso":"eng"}],"day":"01","year":"2022","status":"public","date_published":"2022-11-01T00:00:00Z","publication":"Annales Henri Poincaré","citation":{"apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. Springer Nature. https://doi.org/10.1007/s00023-022-01188-8","ama":"Cipolloni G, Erdös L, Schröder DJ. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 2022;23(11):3981-4002. doi:10.1007/s00023-022-01188-8","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Annales Henri Poincaré 23 (2022) 3981–4002.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré. Springer Nature, 2022. https://doi.org/10.1007/s00023-022-01188-8.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Density of small singular values of the shifted real Ginibre ensemble. Annales Henri Poincaré. 23(11), 3981–4002.","mla":"Cipolloni, Giorgio, et al. “Density of Small Singular Values of the Shifted Real Ginibre Ensemble.” Annales Henri Poincaré, vol. 23, no. 11, Springer Nature, 2022, pp. 3981–4002, doi:10.1007/s00023-022-01188-8.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Density of small singular values of the shifted real Ginibre ensemble,” Annales Henri Poincaré, vol. 23, no. 11. Springer Nature, pp. 3981–4002, 2022."},"intvolume":" 23","file_date_updated":"2023-01-27T11:06:47Z","month":"11","oa_version":"Published Version","scopus_import":"1","type":"journal_article","doi":"10.1007/s00023-022-01188-8","article_processing_charge":"No","page":"3981-4002","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publication_status":"published","file":[{"checksum":"5582f059feeb2f63e2eb68197a34d7dc","date_created":"2023-01-27T11:06:47Z","file_size":1333638,"date_updated":"2023-01-27T11:06:47Z","relation":"main_file","creator":"dernst","file_id":"12424","file_name":"2022_AnnalesHenriP_Cipolloni.pdf","success":1,"access_level":"open_access","content_type":"application/pdf"}],"isi":1,"title":"Density of small singular values of the shifted real Ginibre ensemble","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","quality_controlled":"1","keyword":["Mathematical Physics","Nuclear and High Energy Physics","Statistical and Nonlinear Physics"],"_id":"12232","publisher":"Springer Nature","date_created":"2023-01-16T09:50:26Z","acknowledgement":"Open access funding provided by Swiss Federal Institute of Technology Zurich. Supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","external_id":{"isi":["000796323500001"]},"date_updated":"2023-08-04T09:33:52Z","abstract":[{"text":"We derive a precise asymptotic formula for the density of the small singular values of the real Ginibre matrix ensemble shifted by a complex parameter z as the dimension tends to infinity. For z away from the real axis the formula coincides with that for the complex Ginibre ensemble we derived earlier in Cipolloni et al. (Prob Math Phys 1:101–146, 2020). On the level of the one-point function of the low lying singular values we thus confirm the transition from real to complex Ginibre ensembles as the shift parameter z becomes genuinely complex; the analogous phenomenon has been well known for eigenvalues. We use the superbosonization formula (Littelmann et al. in Comm Math Phys 283:343–395, 2008) in a regime where the main contribution comes from a three dimensional saddle manifold.","lang":"eng"}],"ddc":["510"],"publication_identifier":{"issn":["1424-0637"],"eissn":["1424-0661"]},"issue":"11","oa":1},{"publication_identifier":{"issn":["0022-2488"],"eissn":["1089-7658"]},"ec_funded":1,"abstract":[{"text":"We consider the eigenvalues of a large dimensional real or complex Ginibre matrix in the region of the complex plane where their real parts reach their maximum value. This maximum follows the Gumbel distribution and that these extreme eigenvalues form a Poisson point process as the dimension asymptotically tends to infinity. In the complex case, these facts have already been established by Bender [Probab. Theory Relat. Fields 147, 241 (2010)] and in the real case by Akemann and Phillips [J. Stat. Phys. 155, 421 (2014)] even for the more general elliptic ensemble with a sophisticated saddle point analysis. The purpose of this article is to give a very short direct proof in the Ginibre case with an effective error term. Moreover, our estimates on the correlation kernel in this regime serve as a key input for accurately locating [Formula: see text] for any large matrix X with i.i.d. entries in the companion paper [G. Cipolloni et al., arXiv:2206.04448 (2022)]. ","lang":"eng"}],"ddc":["510","530"],"oa":1,"project":[{"grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta","_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020"}],"issue":"10","date_created":"2023-01-16T09:52:58Z","publisher":"AIP Publishing","date_updated":"2023-08-04T09:40:02Z","external_id":{"arxiv":["2206.04443"],"isi":["000869715800001"]},"acknowledgement":"The authors are grateful to G. Akemann for bringing Refs. 19 and 24–26 to their attention. Discussions with Guillaume Dubach on a preliminary version of this project are acknowledged.\r\nL.E. and Y.X. were supported by the ERC Advanced Grant “RMTBeyond” under Grant No. 101020331. D.S. was supported by Dr. Max Rössler, the Walter Haefner Foundation, and the ETH Zürich Foundation.","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"quality_controlled":"1","_id":"12243","isi":1,"file":[{"date_updated":"2023-01-30T08:01:10Z","relation":"main_file","file_id":"12436","creator":"dernst","file_size":7356807,"checksum":"2db278ae5b07f345a7e3fec1f92b5c33","date_created":"2023-01-30T08:01:10Z","success":1,"access_level":"open_access","content_type":"application/pdf","file_name":"2022_JourMathPhysics_Cipolloni2.pdf"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"Directional extremal statistics for Ginibre eigenvalues","article_processing_charge":"Yes (via OA deal)","type":"journal_article","doi":"10.1063/5.0104290","publication_status":"published","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa_version":"Published Version","scopus_import":"1","intvolume":" 63","month":"10","file_date_updated":"2023-01-30T08:01:10Z","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Y. Xu, Journal of Mathematical Physics 63 (2022).","apa":"Cipolloni, G., Erdös, L., Schröder, D. J., & Xu, Y. (2022). Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. AIP Publishing. https://doi.org/10.1063/5.0104290","ama":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 2022;63(10). doi:10.1063/5.0104290","chicago":"Cipolloni, Giorgio, László Erdös, Dominik J Schröder, and Yuanyuan Xu. “Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical Physics. AIP Publishing, 2022. https://doi.org/10.1063/5.0104290.","mla":"Cipolloni, Giorgio, et al. “Directional Extremal Statistics for Ginibre Eigenvalues.” Journal of Mathematical Physics, vol. 63, no. 10, 103303, AIP Publishing, 2022, doi:10.1063/5.0104290.","ieee":"G. Cipolloni, L. Erdös, D. J. Schröder, and Y. Xu, “Directional extremal statistics for Ginibre eigenvalues,” Journal of Mathematical Physics, vol. 63, no. 10. AIP Publishing, 2022.","ista":"Cipolloni G, Erdös L, Schröder DJ, Xu Y. 2022. Directional extremal statistics for Ginibre eigenvalues. Journal of Mathematical Physics. 63(10), 103303."},"publication":"Journal of Mathematical Physics","date_published":"2022-10-14T00:00:00Z","has_accepted_license":"1","article_type":"original","status":"public","language":[{"iso":"eng"}],"day":"14","year":"2022","department":[{"_id":"LaEr"}],"volume":63,"author":[{"orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87"},{"id":"7902bdb1-a2a4-11eb-a164-c9216f71aea3","last_name":"Xu","first_name":"Yuanyuan","full_name":"Xu, Yuanyuan"}],"article_number":"103303"},{"oa":1,"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","call_identifier":"H2020","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"abstract":[{"lang":"eng","text":"We prove local laws, i.e. optimal concentration estimates for arbitrary products of resolvents of a Wigner random matrix with deterministic matrices in between. We find that the size of such products heavily depends on whether some of the deterministic matrices are traceless. Our estimates correctly account for this dependence and they hold optimally down to the smallest possible spectral scale."}],"ddc":["510"],"ec_funded":1,"publication_identifier":{"eissn":["1083-6489"]},"acknowledgement":"L. Erdős was supported by ERC Advanced Grant “RMTBeyond” No. 101020331. D. Schröder was supported by Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zürich Foundation.","external_id":{"isi":["000910863700003"]},"date_updated":"2023-08-04T10:32:23Z","publisher":"Institute of Mathematical Statistics","date_created":"2023-01-16T10:04:38Z","_id":"12290","quality_controlled":"1","keyword":["Statistics","Probability and Uncertainty","Statistics and Probability"],"title":"Optimal multi-resolvent local laws for Wigner matrices","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"content_type":"application/pdf","success":1,"access_level":"open_access","file_name":"2022_ElecJournProbability_Cipolloni.pdf","creator":"dernst","file_id":"12464","relation":"main_file","date_updated":"2023-01-30T11:59:21Z","checksum":"bb647b48fbdb59361210e425c220cdcb","date_created":"2023-01-30T11:59:21Z","file_size":502149}],"isi":1,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"page":"1-38","publication_status":"published","doi":"10.1214/22-ejp838","type":"journal_article","article_processing_charge":"No","date_published":"2022-09-12T00:00:00Z","publication":"Electronic Journal of Probability","citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 27 (2022) 1–38.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2022). Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/22-ejp838","ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 2022;27:1-38. doi:10.1214/22-ejp838","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2022. https://doi.org/10.1214/22-ejp838.","mla":"Cipolloni, Giorgio, et al. “Optimal Multi-Resolvent Local Laws for Wigner Matrices.” Electronic Journal of Probability, vol. 27, Institute of Mathematical Statistics, 2022, pp. 1–38, doi:10.1214/22-ejp838.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2022. Optimal multi-resolvent local laws for Wigner matrices. Electronic Journal of Probability. 27, 1–38.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal multi-resolvent local laws for Wigner matrices,” Electronic Journal of Probability, vol. 27. Institute of Mathematical Statistics, pp. 1–38, 2022."},"file_date_updated":"2023-01-30T11:59:21Z","intvolume":" 27","month":"09","oa_version":"Published Version","scopus_import":"1","year":"2022","language":[{"iso":"eng"}],"day":"12","status":"public","article_type":"original","has_accepted_license":"1","author":[{"last_name":"Cipolloni","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","first_name":"Dominik J","orcid":"0000-0002-2904-1856"}],"volume":27,"department":[{"_id":"LaEr"}]},{"language":[{"iso":"eng"}],"day":"29","year":"2022","status":"public","has_accepted_license":"1","article_type":"original","author":[{"first_name":"Sven Joscha","full_name":"Henheik, Sven Joscha","orcid":"0000-0003-1106-327X","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","last_name":"Henheik"},{"last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard","first_name":"Asbjørn Bækgaard"}],"article_number":"5","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"volume":189,"tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"publication_status":"published","article_processing_charge":"Yes (via OA deal)","type":"journal_article","doi":"10.1007/s10955-022-02965-9","month":"07","intvolume":" 189","file_date_updated":"2022-08-08T07:36:34Z","scopus_import":"1","oa_version":"Published Version","date_published":"2022-07-29T00:00:00Z","publication":"Journal of Statistical Physics","citation":{"chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02965-9.","short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022).","apa":"Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9","ama":"Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9","mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature, 2022, doi:10.1007/s10955-022-02965-9.","ista":"Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5.","ieee":"S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal of Statistical Physics, vol. 189. Springer Nature, 2022."},"_id":"11732","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"quality_controlled":"1","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","title":"The BCS energy gap at high density","file":[{"file_name":"2022_JourStatisticalPhysics_Henheik.pdf","content_type":"application/pdf","success":1,"access_level":"open_access","file_size":419563,"date_created":"2022-08-08T07:36:34Z","checksum":"b398c4dbf65f71d417981d6e366427e9","file_id":"11746","creator":"dernst","date_updated":"2022-08-08T07:36:34Z","relation":"main_file"}],"isi":1,"project":[{"call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331","name":"Random matrices beyond Wigner-Dyson-Mehta"}],"oa":1,"publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"ddc":["530"],"abstract":[{"text":"We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature.","lang":"eng"}],"ec_funded":1,"external_id":{"isi":["000833007200002"]},"date_updated":"2023-09-05T14:57:49Z","acknowledgement":"We are grateful to Robert Seiringer for helpful discussions and many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open access funding provided by Institute of Science and Technology (IST Austria)","publisher":"Springer Nature","date_created":"2022-08-05T11:36:56Z"},{"file":[{"checksum":"1c975afb31460277ce4d22b93538e5f9","date_created":"2021-11-15T10:10:17Z","file_size":735940,"creator":"cchlebak","file_id":"10288","date_updated":"2021-11-15T10:10:17Z","relation":"main_file","file_name":"2021_ElecJournalProb_Dubach.pdf","content_type":"application/pdf","success":1,"access_level":"open_access"}],"title":"On eigenvector statistics in the spherical and truncated unitary ensembles","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","quality_controlled":"1","_id":"10285","date_created":"2021-11-14T23:01:25Z","publisher":"Institute of Mathematical Statistics","acknowledgement":"We acknowledge partial support from the grants NSF DMS-1812114 of P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI). This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We would like to thank Paul Bourgade and László Erdős for many helpful comments.","date_updated":"2021-11-15T10:48:46Z","ec_funded":1,"abstract":[{"text":"We study the overlaps between right and left eigenvectors for random matrices of the spherical ensemble, as well as truncated unitary ensembles in the regime where half of the matrix at least is truncated. These two integrable models exhibit a form of duality, and the essential steps of our investigation can therefore be performed in parallel. In every case, conditionally on all eigenvalues, diagonal overlaps are shown to be distributed as a product of independent random variables with explicit distributions. This enables us to prove that the scaled diagonal overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail limit, namely, the inverse of a γ2 distribution. We also provide formulae for the conditional expectation of diagonal and off-diagonal overlaps, either with respect to one eigenvalue, or with respect to the whole spectrum. These results, analogous to what is known for the complex Ginibre ensemble, can be obtained in these cases thanks to integration techniques inspired from a previous work by Forrester & Krishnapur.","lang":"eng"}],"ddc":["519"],"publication_identifier":{"eissn":["1083-6489"]},"oa":1,"project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"volume":26,"department":[{"_id":"LaEr"}],"article_number":"124","author":[{"full_name":"Dubach, Guillaume","first_name":"Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"}],"article_type":"original","has_accepted_license":"1","status":"public","year":"2021","language":[{"iso":"eng"}],"day":"28","citation":{"chicago":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP686.","ama":"Dubach G. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP686","apa":"Dubach, G. (2021). On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP686","short":"G. Dubach, Electronic Journal of Probability 26 (2021).","mla":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” Electronic Journal of Probability, vol. 26, 124, Institute of Mathematical Statistics, 2021, doi:10.1214/21-EJP686.","ieee":"G. Dubach, “On eigenvector statistics in the spherical and truncated unitary ensembles,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021.","ista":"Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 26, 124."},"publication":"Electronic Journal of Probability","date_published":"2021-09-28T00:00:00Z","oa_version":"Published Version","scopus_import":"1","month":"09","file_date_updated":"2021-11-15T10:10:17Z","intvolume":" 26","type":"journal_article","doi":"10.1214/21-EJP686","article_processing_charge":"No","publication_status":"published","tmp":{"image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"}},{"publication":"arXiv","date_published":"2021-03-08T00:00:00Z","citation":{"chicago":"Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.04817.","apa":"Arguin, L.-P., Dubach, G., & Hartung, L. (n.d.). Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv. https://doi.org/10.48550/arXiv.2103.04817","ama":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv. doi:10.48550/arXiv.2103.04817","short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).","ista":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv, 2103.04817.","mla":"Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” ArXiv, 2103.04817, doi:10.48550/arXiv.2103.04817.","ieee":"L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the Riemann zeta function over intervals of varying length,” arXiv. ."},"month":"03","oa_version":"Preprint","date_created":"2021-03-09T11:08:15Z","acknowledgement":"The research of L.-P. A. is supported in part by the grant NSF CAREER DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID 443891315 within SPP 2265 and Project-ID 446173099.","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.04817"}],"external_id":{"arxiv":["2103.04817"]},"date_updated":"2023-05-03T10:22:59Z","abstract":[{"text":"We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length (log T)θ, where θ is either fixed or tends to zero at a suitable rate.\r\nIt is shown that the deterministic level of the maximum interpolates smoothly between the ones\r\nof log-correlated variables and of i.i.d. random variables, exhibiting a smooth transition ‘from\r\n3/4 to 1/4’ in the second order. This provides a natural context where extreme value statistics of\r\nlog-correlated variables with time-dependent variance and rate occur. A key ingredient of the\r\nproof is a precise upper tail tightness estimate for the maximum of the model on intervals of\r\nsize one, that includes a Gaussian correction. This correction is expected to be present for the\r\nRiemann zeta function and pertains to the question of the correct order of the maximum of\r\nthe zeta function in large intervals.","lang":"eng"}],"ec_funded":1,"doi":"10.48550/arXiv.2103.04817","type":"preprint","article_processing_charge":"No","publication_status":"submitted","oa":1,"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"department":[{"_id":"LaEr"}],"article_number":"2103.04817","title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","author":[{"full_name":"Arguin, Louis-Pierre","first_name":"Louis-Pierre","last_name":"Arguin"},{"first_name":"Guillaume","full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach"},{"full_name":"Hartung, Lisa","first_name":"Lisa","last_name":"Hartung"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","day":"08","language":[{"iso":"eng"}],"year":"2021","status":"public","_id":"9230"},{"_id":"9281","status":"public","day":"21","language":[{"iso":"eng"}],"year":"2021","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","author":[{"full_name":"Dubach, Guillaume","first_name":"Guillaume","orcid":"0000-0001-6892-8137","last_name":"Dubach","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"},{"id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425","last_name":"Mühlböck","orcid":"0000-0003-1548-0177","first_name":"Fabian","full_name":"Mühlböck, Fabian"}],"title":"Formal verification of Zagier's one-sentence proof","article_number":"2103.11389","department":[{"_id":"LaEr"},{"_id":"ToHe"}],"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships"}],"oa":1,"related_material":{"record":[{"relation":"other","status":"public","id":"9946"}]},"publication_status":"submitted","article_processing_charge":"No","ec_funded":1,"doi":"10.48550/arXiv.2103.11389","type":"preprint","abstract":[{"lang":"eng","text":"We comment on two formal proofs of Fermat's sum of two squares theorem, written using the Mathematical Components libraries of the Coq proof assistant. The first one follows Zagier's celebrated one-sentence proof; the second follows David Christopher's recent new proof relying on partition-theoretic arguments. Both formal proofs rely on a general property of involutions of finite sets, of independent interest. The proof technique consists for the most part of automating recurrent tasks (such as case distinctions and computations on natural numbers) via ad hoc tactics."}],"date_updated":"2023-05-03T10:26:45Z","external_id":{"arxiv":["2103.11389"]},"main_file_link":[{"url":"https://arxiv.org/abs/2103.11389","open_access":"1"}],"oa_version":"Preprint","date_created":"2021-03-23T05:38:48Z","month":"03","citation":{"chicago":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.11389.","apa":"Dubach, G., & Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence proof. arXiv. https://doi.org/10.48550/arXiv.2103.11389","ama":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv. doi:10.48550/arXiv.2103.11389","short":"G. Dubach, F. Mühlböck, ArXiv (n.d.).","ista":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv, 2103.11389.","ieee":"G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,” arXiv. .","mla":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” ArXiv, 2103.11389, doi:10.48550/arXiv.2103.11389."},"date_published":"2021-03-21T00:00:00Z","publication":"arXiv"},{"external_id":{"isi":["000581730500011"],"arxiv":["2002.11678"]},"date_updated":"2023-08-04T10:58:14Z","main_file_link":[{"url":"https://arxiv.org/abs/2002.11678","open_access":"1"}],"acknowledgement":"The authors are grateful to Milán Mosonyi for fruitful discussions on the topic, and to the anonymous referee for his/her comments and suggestions.\r\nJ. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant for Quantum Information Theory, No. 96 141, and by Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K119442, no. K124152, and no. KH129601. D. Virosztek was supported by the ISTFELLOW program of the Institute of Science and Technology Austria (project code IC1027FELL01), by the European Union's Horizon 2020 research and innovation program under the Marie Sklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National Research, Development and Innovation Office (NKFIH) via grants no. K124152, and no. KH129601.","publisher":"Elsevier","date_created":"2020-09-11T08:35:50Z","project":[{"call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425","grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability"},{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"oa":1,"publication_identifier":{"issn":["0024-3795"]},"abstract":[{"lang":"eng","text":"It is well known that special Kubo-Ando operator means admit divergence center interpretations, moreover, they are also mean squared error estimators for certain metrics on positive definite operators. In this paper we give a divergence center interpretation for every symmetric Kubo-Ando mean. This characterization of the symmetric means naturally leads to a definition of weighted and multivariate versions of a large class of symmetric Kubo-Ando means. We study elementary properties of these weighted multivariate means, and note in particular that in the special case of the geometric mean we recover the weighted A#H-mean introduced by Kim, Lawson, and Lim."}],"ec_funded":1,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","isi":1,"_id":"8373","keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"quality_controlled":"1","month":"01","intvolume":" 609","oa_version":"Preprint","date_published":"2021-01-15T00:00:00Z","publication":"Linear Algebra and its Applications","citation":{"mla":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” Linear Algebra and Its Applications, vol. 609, Elsevier, 2021, pp. 203–17, doi:10.1016/j.laa.2020.09.007.","ista":"Pitrik J, Virosztek D. 2021. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 609, 203–217.","ieee":"J. Pitrik and D. Virosztek, “A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means,” Linear Algebra and its Applications, vol. 609. Elsevier, pp. 203–217, 2021.","short":"J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.","apa":"Pitrik, J., & Virosztek, D. (2021). A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and Its Applications. Elsevier. https://doi.org/10.1016/j.laa.2020.09.007","ama":"Pitrik J, Virosztek D. A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means. Linear Algebra and its Applications. 2021;609:203-217. doi:10.1016/j.laa.2020.09.007","chicago":"Pitrik, József, and Daniel Virosztek. “A Divergence Center Interpretation of General Symmetric Kubo-Ando Means, and Related Weighted Multivariate Operator Means.” Linear Algebra and Its Applications. Elsevier, 2021. https://doi.org/10.1016/j.laa.2020.09.007."},"page":"203-217","publication_status":"published","article_processing_charge":"No","type":"journal_article","doi":"10.1016/j.laa.2020.09.007","author":[{"last_name":"Pitrik","full_name":"Pitrik, József","first_name":"József"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","last_name":"Virosztek","orcid":"0000-0003-1109-5511","first_name":"Daniel","full_name":"Virosztek, Daniel"}],"department":[{"_id":"LaEr"}],"volume":609,"language":[{"iso":"eng"}],"year":"2021","day":"15","status":"public","article_type":"original"}]