[{"doi":"10.1007/s10955-022-02965-9","language":[{"iso":"eng"}],"oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"external_id":{"isi":["000833007200002"]},"project":[{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"quality_controlled":"1","isi":1,"publication_identifier":{"eissn":["1572-9613"],"issn":["0022-4715"]},"month":"07","author":[{"full_name":"Henheik, Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb","orcid":"0000-0003-1106-327X","first_name":"Sven Joscha","last_name":"Henheik"},{"first_name":"Asbjørn Bækgaard","last_name":"Lauritsen","id":"e1a2682f-dc8d-11ea-abe3-81da9ac728f1","orcid":"0000-0003-4476-2288","full_name":"Lauritsen, Asbjørn Bækgaard"}],"volume":189,"date_updated":"2023-09-05T14:57:49Z","date_created":"2022-08-05T11:36:56Z","acknowledgement":"We are grateful to Robert Seiringer for helpful discussions and many valuable comments\r\non an earlier version of the manuscript. J.H. acknowledges partial financial support by the ERC Advanced Grant “RMTBeyond’ No. 101020331. Open access funding provided by Institute of Science and Technology (IST Austria)","year":"2022","publisher":"Springer Nature","department":[{"_id":"GradSch"},{"_id":"LaEr"},{"_id":"RoSe"}],"publication_status":"published","ec_funded":1,"file_date_updated":"2022-08-08T07:36:34Z","article_number":"5","date_published":"2022-07-29T00:00:00Z","citation":{"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.","apa":"Henheik, S. J., & Lauritsen, A. B. (2022). The BCS energy gap at high density. Journal of Statistical Physics. Springer Nature. https://doi.org/10.1007/s10955-022-02965-9","ama":"Henheik SJ, Lauritsen AB. The BCS energy gap at high density. Journal of Statistical Physics. 2022;189. doi:10.1007/s10955-022-02965-9","chicago":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics. Springer Nature, 2022. https://doi.org/10.1007/s10955-022-02965-9.","mla":"Henheik, Sven Joscha, and Asbjørn Bækgaard Lauritsen. “The BCS Energy Gap at High Density.” Journal of Statistical Physics, vol. 189, 5, Springer Nature, 2022, doi:10.1007/s10955-022-02965-9.","short":"S.J. Henheik, A.B. Lauritsen, Journal of Statistical Physics 189 (2022)."},"publication":"Journal of Statistical Physics","article_type":"original","article_processing_charge":"Yes (via OA deal)","has_accepted_license":"1","day":"29","scopus_import":"1","keyword":["Mathematical Physics","Statistical and Nonlinear Physics"],"oa_version":"Published Version","file":[{"file_id":"11746","relation":"main_file","success":1,"checksum":"b398c4dbf65f71d417981d6e366427e9","date_created":"2022-08-08T07:36:34Z","date_updated":"2022-08-08T07:36:34Z","access_level":"open_access","file_name":"2022_JourStatisticalPhysics_Henheik.pdf","creator":"dernst","content_type":"application/pdf","file_size":419563}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","_id":"11732","intvolume":" 189","status":"public","ddc":["530"],"title":"The BCS energy gap at high density","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"}],"type":"journal_article"},{"article_number":"124","ec_funded":1,"file_date_updated":"2021-11-15T10:10:17Z","publisher":"Institute of Mathematical Statistics","department":[{"_id":"LaEr"}],"publication_status":"published","year":"2021","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.","volume":26,"date_created":"2021-11-14T23:01:25Z","date_updated":"2021-11-15T10:48:46Z","author":[{"full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137","first_name":"Guillaume","last_name":"Dubach"}],"publication_identifier":{"eissn":["1083-6489"]},"month":"09","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"quality_controlled":"1","oa":1,"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png"},"language":[{"iso":"eng"}],"doi":"10.1214/21-EJP686","type":"journal_article","abstract":[{"lang":"eng","text":"We study the overlaps between right and left eigenvectors for random matrices of the spherical ensemble, as well as truncated unitary ensembles in the regime where half of the matrix at least is truncated. These two integrable models exhibit a form of duality, and the essential steps of our investigation can therefore be performed in parallel. In every case, conditionally on all eigenvalues, diagonal overlaps are shown to be distributed as a product of independent random variables with explicit distributions. This enables us to prove that the scaled diagonal overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail limit, namely, the inverse of a γ2 distribution. We also provide formulae for the conditional expectation of diagonal and off-diagonal overlaps, either with respect to one eigenvalue, or with respect to the whole spectrum. These results, analogous to what is known for the complex Ginibre ensemble, can be obtained in these cases thanks to integration techniques inspired from a previous work by Forrester & Krishnapur."}],"intvolume":" 26","ddc":["519"],"status":"public","title":"On eigenvector statistics in the spherical and truncated unitary ensembles","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","_id":"10285","file":[{"file_size":735940,"content_type":"application/pdf","creator":"cchlebak","access_level":"open_access","file_name":"2021_ElecJournalProb_Dubach.pdf","checksum":"1c975afb31460277ce4d22b93538e5f9","success":1,"date_created":"2021-11-15T10:10:17Z","date_updated":"2021-11-15T10:10:17Z","relation":"main_file","file_id":"10288"}],"oa_version":"Published Version","scopus_import":"1","article_processing_charge":"No","has_accepted_license":"1","day":"28","article_type":"original","citation":{"ama":"Dubach G. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP686","ista":"Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 26, 124.","ieee":"G. Dubach, “On eigenvector statistics in the spherical and truncated unitary ensembles,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021.","apa":"Dubach, G. (2021). On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP686","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.","short":"G. Dubach, Electronic Journal of Probability 26 (2021).","chicago":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP686."},"publication":"Electronic Journal of Probability","date_published":"2021-09-28T00:00:00Z"},{"ec_funded":1,"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"}],"type":"preprint","article_number":"2103.04817","author":[{"first_name":"Louis-Pierre","last_name":"Arguin","full_name":"Arguin, Louis-Pierre"},{"full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137","first_name":"Guillaume","last_name":"Dubach"},{"full_name":"Hartung, Lisa","last_name":"Hartung","first_name":"Lisa"}],"oa_version":"Preprint","date_updated":"2023-05-03T10:22:59Z","date_created":"2021-03-09T11:08:15Z","_id":"9230","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.","year":"2021","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"status":"public","title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","publication_status":"submitted","article_processing_charge":"No","day":"08","month":"03","date_published":"2021-03-08T00:00:00Z","doi":"10.48550/arXiv.2103.04817","language":[{"iso":"eng"}],"oa":1,"citation":{"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","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. .","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","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.","short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).","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.","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."},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.04817"}],"external_id":{"arxiv":["2103.04817"]},"publication":"arXiv","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"}]},{"abstract":[{"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.","lang":"eng"}],"ec_funded":1,"article_number":"2103.11389","type":"preprint","date_updated":"2023-05-03T10:26:45Z","date_created":"2021-03-23T05:38:48Z","oa_version":"Preprint","author":[{"orcid":"0000-0001-6892-8137","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach","first_name":"Guillaume","full_name":"Dubach, Guillaume"},{"full_name":"Mühlböck, Fabian","orcid":"0000-0003-1548-0177","id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425","last_name":"Mühlböck","first_name":"Fabian"}],"related_material":{"record":[{"relation":"other","status":"public","id":"9946"}]},"publication_status":"submitted","title":"Formal verification of Zagier's one-sentence proof","status":"public","department":[{"_id":"LaEr"},{"_id":"ToHe"}],"year":"2021","_id":"9281","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"03","day":"21","article_processing_charge":"No","language":[{"iso":"eng"}],"date_published":"2021-03-21T00:00:00Z","doi":"10.48550/arXiv.2103.11389","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","_id":"260C2330-B435-11E9-9278-68D0E5697425","grant_number":"754411"}],"publication":"arXiv","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.11389"}],"external_id":{"arxiv":["2103.11389"]},"citation":{"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. .","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","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.","mla":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” ArXiv, 2103.11389, doi:10.48550/arXiv.2103.11389.","short":"G. Dubach, F. Mühlböck, ArXiv (n.d.)."}},{"ec_funded":1,"author":[{"last_name":"Pitrik","first_name":"József","full_name":"Pitrik, József"},{"full_name":"Virosztek, Daniel","last_name":"Virosztek","first_name":"Daniel","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"date_updated":"2023-08-04T10:58:14Z","date_created":"2020-09-11T08:35:50Z","volume":609,"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.","year":"2021","publication_status":"published","publisher":"Elsevier","department":[{"_id":"LaEr"}],"month":"01","publication_identifier":{"issn":["0024-3795"]},"doi":"10.1016/j.laa.2020.09.007","language":[{"iso":"eng"}],"main_file_link":[{"url":"https://arxiv.org/abs/2002.11678","open_access":"1"}],"external_id":{"arxiv":["2002.11678"],"isi":["000581730500011"]},"oa":1,"isi":1,"quality_controlled":"1","project":[{"call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294","_id":"26A455A6-B435-11E9-9278-68D0E5697425"},{"grant_number":"291734","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme"}],"abstract":[{"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.","lang":"eng"}],"type":"journal_article","oa_version":"Preprint","_id":"8373","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","title":"A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means","intvolume":" 609","day":"15","article_processing_charge":"No","keyword":["Kubo-Ando mean","weighted multivariate mean","barycenter"],"date_published":"2021-01-15T00:00:00Z","publication":"Linear Algebra and its Applications","citation":{"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","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","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.","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.","short":"J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217.","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.","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."},"article_type":"original","page":"203-217"}]