--- _id: '11732' abstract: - lang: eng text: We study the BCS energy gap Ξ in the high–density limit and derive an asymptotic formula, which strongly depends on the strength of the interaction potential V on the Fermi surface. In combination with the recent result by one of us (Math. Phys. Anal. Geom. 25, 3, 2022) on the critical temperature Tc at high densities, we prove the universality of the ratio of the energy gap and the critical temperature. 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)" article_number: '5' article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Sven Joscha full_name: Henheik, Sven Joscha id: 31d731d7-d235-11ea-ad11-b50331c8d7fb last_name: Henheik orcid: 0000-0003-1106-327X - first_name: Asbjørn Bækgaard full_name: Lauritsen, Asbjørn Bækgaard id: e1a2682f-dc8d-11ea-abe3-81da9ac728f1 last_name: Lauritsen orcid: 0000-0003-4476-2288 citation: 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 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 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. ieee: S. J. Henheik and A. B. Lauritsen, “The BCS energy gap at high density,” Journal of Statistical Physics, vol. 189. Springer Nature, 2022. ista: Henheik SJ, Lauritsen AB. 2022. The BCS energy gap at high density. Journal of Statistical Physics. 189, 5. 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). date_created: 2022-08-05T11:36:56Z date_published: 2022-07-29T00:00:00Z date_updated: 2023-09-05T14:57:49Z day: '29' ddc: - '530' department: - _id: GradSch - _id: LaEr - _id: RoSe doi: 10.1007/s10955-022-02965-9 ec_funded: 1 external_id: isi: - '000833007200002' file: - access_level: open_access checksum: b398c4dbf65f71d417981d6e366427e9 content_type: application/pdf creator: dernst date_created: 2022-08-08T07:36:34Z date_updated: 2022-08-08T07:36:34Z file_id: '11746' file_name: 2022_JourStatisticalPhysics_Henheik.pdf file_size: 419563 relation: main_file success: 1 file_date_updated: 2022-08-08T07:36:34Z has_accepted_license: '1' intvolume: ' 189' isi: 1 keyword: - Mathematical Physics - Statistical and Nonlinear Physics language: - iso: eng month: '07' oa: 1 oa_version: Published Version project: - _id: 62796744-2b32-11ec-9570-940b20777f1d call_identifier: H2020 grant_number: '101020331' name: Random matrices beyond Wigner-Dyson-Mehta publication: Journal of Statistical Physics publication_identifier: eissn: - 1572-9613 issn: - 0022-4715 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: The BCS energy gap at high density tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1 volume: 189 year: '2022' ... --- _id: '10285' 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. 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. article_number: '124' article_processing_charge: No article_type: original author: - first_name: Guillaume full_name: Dubach, Guillaume id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E last_name: Dubach orcid: 0000-0001-6892-8137 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 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 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. 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. 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). date_created: 2021-11-14T23:01:25Z date_published: 2021-09-28T00:00:00Z date_updated: 2021-11-15T10:48:46Z day: '28' ddc: - '519' department: - _id: LaEr doi: 10.1214/21-EJP686 ec_funded: 1 file: - access_level: open_access checksum: 1c975afb31460277ce4d22b93538e5f9 content_type: application/pdf creator: cchlebak date_created: 2021-11-15T10:10:17Z date_updated: 2021-11-15T10:10:17Z file_id: '10288' file_name: 2021_ElecJournalProb_Dubach.pdf file_size: 735940 relation: main_file success: 1 file_date_updated: 2021-11-15T10:10:17Z has_accepted_license: '1' intvolume: ' 26' language: - iso: eng month: '09' oa: 1 oa_version: Published Version project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: Electronic Journal of Probability publication_identifier: eissn: - 1083-6489 publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: On eigenvector statistics in the spherical and truncated unitary ensembles tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9 volume: 26 year: '2021' ... --- _id: '9230' abstract: - lang: eng 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." 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. article_number: '2103.04817' article_processing_charge: No author: - first_name: Louis-Pierre full_name: Arguin, Louis-Pierre last_name: Arguin - first_name: Guillaume full_name: Dubach, Guillaume id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E last_name: Dubach orcid: 0000-0001-6892-8137 - first_name: Lisa full_name: Hartung, Lisa last_name: Hartung 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 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 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. 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. . 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. short: L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.). date_created: 2021-03-09T11:08:15Z date_published: 2021-03-08T00:00:00Z date_updated: 2023-05-03T10:22:59Z day: '08' department: - _id: LaEr doi: 10.48550/arXiv.2103.04817 ec_funded: 1 external_id: arxiv: - '2103.04817' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2103.04817 month: '03' oa: 1 oa_version: Preprint project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: arXiv publication_status: submitted status: public title: Maxima of a random model of the Riemann zeta function over intervals of varying length type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '9281' 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. article_number: '2103.11389' article_processing_charge: No author: - first_name: Guillaume full_name: Dubach, Guillaume id: D5C6A458-10C4-11EA-ABF4-A4B43DDC885E last_name: Dubach orcid: 0000-0001-6892-8137 - first_name: Fabian full_name: Mühlböck, Fabian id: 6395C5F6-89DF-11E9-9C97-6BDFE5697425 last_name: Mühlböck orcid: 0000-0003-1548-0177 citation: ama: Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv. doi:10.48550/arXiv.2103.11389 apa: Dubach, G., & Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence proof. arXiv. https://doi.org/10.48550/arXiv.2103.11389 chicago: Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2103.11389. ieee: G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,” arXiv. . ista: Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. 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.). date_created: 2021-03-23T05:38:48Z date_published: 2021-03-21T00:00:00Z date_updated: 2023-05-03T10:26:45Z day: '21' department: - _id: LaEr - _id: ToHe doi: 10.48550/arXiv.2103.11389 ec_funded: 1 external_id: arxiv: - '2103.11389' language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2103.11389 month: '03' oa: 1 oa_version: Preprint project: - _id: 260C2330-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '754411' name: ISTplus - Postdoctoral Fellowships publication: arXiv publication_status: submitted related_material: record: - id: '9946' relation: other status: public status: public title: Formal verification of Zagier's one-sentence proof type: preprint user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87 year: '2021' ... --- _id: '8373' 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. 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." article_processing_charge: No article_type: original author: - first_name: József full_name: Pitrik, József last_name: Pitrik - first_name: Daniel full_name: Virosztek, Daniel id: 48DB45DA-F248-11E8-B48F-1D18A9856A87 last_name: Virosztek orcid: 0000-0003-1109-5511 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 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. 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. 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. short: J. Pitrik, D. Virosztek, Linear Algebra and Its Applications 609 (2021) 203–217. date_created: 2020-09-11T08:35:50Z date_published: 2021-01-15T00:00:00Z date_updated: 2023-08-04T10:58:14Z day: '15' department: - _id: LaEr doi: 10.1016/j.laa.2020.09.007 ec_funded: 1 external_id: arxiv: - '2002.11678' isi: - '000581730500011' intvolume: ' 609' isi: 1 keyword: - Kubo-Ando mean - weighted multivariate mean - barycenter language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/2002.11678 month: '01' oa: 1 oa_version: Preprint page: 203-217 project: - _id: 26A455A6-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '846294' name: Geometric study of Wasserstein spaces and free probability - _id: 25681D80-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '291734' name: International IST Postdoc Fellowship Programme publication: Linear Algebra and its Applications publication_identifier: issn: - 0024-3795 publication_status: published publisher: Elsevier quality_controlled: '1' status: public title: A divergence center interpretation of general symmetric Kubo-Ando means, and related weighted multivariate operator means type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 609 year: '2021' ... --- _id: '9036' abstract: - lang: eng text: In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space. acknowledgement: D. Virosztek was supported by the European Union's Horizon 2020 research and innovation programme under the Marie Skłodowska-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. article_number: '107595' article_processing_charge: No article_type: original author: - first_name: Daniel full_name: Virosztek, Daniel id: 48DB45DA-F248-11E8-B48F-1D18A9856A87 last_name: Virosztek orcid: 0000-0003-1109-5511 citation: ama: Virosztek D. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 2021;380(3). doi:10.1016/j.aim.2021.107595 apa: Virosztek, D. (2021). The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107595 chicago: Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107595. ieee: D. Virosztek, “The metric property of the quantum Jensen-Shannon divergence,” Advances in Mathematics, vol. 380, no. 3. Elsevier, 2021. ista: Virosztek D. 2021. The metric property of the quantum Jensen-Shannon divergence. Advances in Mathematics. 380(3), 107595. mla: Virosztek, Daniel. “The Metric Property of the Quantum Jensen-Shannon Divergence.” Advances in Mathematics, vol. 380, no. 3, 107595, Elsevier, 2021, doi:10.1016/j.aim.2021.107595. short: D. Virosztek, Advances in Mathematics 380 (2021). date_created: 2021-01-22T17:55:17Z date_published: 2021-03-26T00:00:00Z date_updated: 2023-08-07T13:34:48Z day: '26' department: - _id: LaEr doi: 10.1016/j.aim.2021.107595 ec_funded: 1 external_id: arxiv: - '1910.10447' isi: - '000619676100035' intvolume: ' 380' isi: 1 issue: '3' keyword: - General Mathematics language: - iso: eng main_file_link: - open_access: '1' url: https://arxiv.org/abs/1910.10447 month: '03' oa: 1 oa_version: Preprint project: - _id: 26A455A6-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '846294' name: Geometric study of Wasserstein spaces and free probability publication: Advances in Mathematics publication_identifier: issn: - 0001-8708 publication_status: published publisher: Elsevier quality_controlled: '1' status: public title: The metric property of the quantum Jensen-Shannon divergence type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 380 year: '2021' ... --- _id: '9412' abstract: - lang: eng text: We extend our recent result [22] on the central limit theorem for the linear eigenvalue statistics of non-Hermitian matrices X with independent, identically distributed complex entries to the real symmetry class. We find that the expectation and variance substantially differ from their complex counterparts, reflecting (i) the special spectral symmetry of real matrices onto the real axis; and (ii) the fact that real i.i.d. matrices have many real eigenvalues. Our result generalizes the previously known special cases where either the test function is analytic [49] or the first four moments of the matrix elements match the real Gaussian [59, 44]. The key element of the proof is the analysis of several weakly dependent Dyson Brownian motions (DBMs). The conceptual novelty of the real case compared with [22] is that the correlation structure of the stochastic differentials in each individual DBM is non-trivial, potentially even jeopardising its well-posedness. article_number: '24' article_processing_charge: No author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: ama: Cipolloni G, Erdös L, Schröder DJ. Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. 2021;26. doi:10.1214/21-EJP591 apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/21-EJP591 chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” Electronic Journal of Probability. Institute of Mathematical Statistics, 2021. https://doi.org/10.1214/21-EJP591. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular law for random matrices with real entries,” Electronic Journal of Probability, vol. 26. Institute of Mathematical Statistics, 2021. ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Fluctuation around the circular law for random matrices with real entries. Electronic Journal of Probability. 26, 24. mla: Cipolloni, Giorgio, et al. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” Electronic Journal of Probability, vol. 26, 24, Institute of Mathematical Statistics, 2021, doi:10.1214/21-EJP591. short: G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 26 (2021). date_created: 2021-05-23T22:01:44Z date_published: 2021-03-23T00:00:00Z date_updated: 2023-08-08T13:39:19Z day: '23' ddc: - '510' department: - _id: LaEr doi: 10.1214/21-EJP591 ec_funded: 1 external_id: arxiv: - '2002.02438' isi: - '000641855600001' file: - access_level: open_access checksum: 864ab003ad4cffea783f65aa8c2ba69f content_type: application/pdf creator: kschuh date_created: 2021-05-25T13:24:19Z date_updated: 2021-05-25T13:24:19Z file_id: '9423' file_name: 2021_EJP_Cipolloni.pdf file_size: 865148 relation: main_file success: 1 file_date_updated: 2021-05-25T13:24:19Z has_accepted_license: '1' intvolume: ' 26' isi: 1 language: - iso: eng month: '03' oa: 1 oa_version: Published Version project: - _id: 2564DBCA-B435-11E9-9278-68D0E5697425 call_identifier: H2020 grant_number: '665385' name: International IST Doctoral Program publication: Electronic Journal of Probability publication_identifier: eissn: - '10836489' publication_status: published publisher: Institute of Mathematical Statistics quality_controlled: '1' scopus_import: '1' status: public title: Fluctuation around the circular law for random matrices with real entries tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 26 year: '2021' ... --- _id: '9550' abstract: - lang: eng text: 'We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices. ' acknowledgement: The first author is supported in part by Hong Kong RGC Grant GRF 16301519 and NSFC 11871425. The second author is supported in part by ERC Advanced Grant RANMAT 338804. The third author is supported in part by Swedish Research Council Grant VR-2017-05195 and the Knut and Alice Wallenberg Foundation article_number: e44 article_processing_charge: No article_type: original author: - first_name: Zhigang full_name: Bao, Zhigang id: 442E6A6C-F248-11E8-B48F-1D18A9856A87 last_name: Bao orcid: 0000-0003-3036-1475 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Kevin full_name: Schnelli, Kevin id: 434AD0AE-F248-11E8-B48F-1D18A9856A87 last_name: Schnelli orcid: 0000-0003-0954-3231 citation: ama: Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 2021;9. doi:10.1017/fms.2021.38 apa: Bao, Z., Erdös, L., & Schnelli, K. (2021). Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. Cambridge University Press. https://doi.org/10.1017/fms.2021.38 chicago: Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma. Cambridge University Press, 2021. https://doi.org/10.1017/fms.2021.38. ieee: Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” Forum of Mathematics, Sigma, vol. 9. Cambridge University Press, 2021. ista: Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44. mla: Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” Forum of Mathematics, Sigma, vol. 9, e44, Cambridge University Press, 2021, doi:10.1017/fms.2021.38. short: Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021). date_created: 2021-06-13T22:01:33Z date_published: 2021-05-27T00:00:00Z date_updated: 2023-08-08T14:03:40Z day: '27' ddc: - '510' department: - _id: LaEr doi: 10.1017/fms.2021.38 ec_funded: 1 external_id: arxiv: - '2008.07061' isi: - '000654960800001' file: - access_level: open_access checksum: 47c986578de132200d41e6d391905519 content_type: application/pdf creator: cziletti date_created: 2021-06-15T14:40:45Z date_updated: 2021-06-15T14:40:45Z file_id: '9555' file_name: 2021_ForumMath_Bao.pdf file_size: 483458 relation: main_file success: 1 file_date_updated: 2021-06-15T14:40:45Z has_accepted_license: '1' intvolume: ' 9' isi: 1 language: - iso: eng month: '05' oa: 1 oa_version: Published Version project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: Forum of Mathematics, Sigma publication_identifier: eissn: - '20505094' publication_status: published publisher: Cambridge University Press quality_controlled: '1' scopus_import: '1' status: public title: Equipartition principle for Wigner matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 9 year: '2021' ... --- _id: '9912' abstract: - lang: eng text: "In the customary random matrix model for transport in quantum dots with M internal degrees of freedom coupled to a chaotic environment via \U0001D441≪\U0001D440 channels, the density \U0001D70C of transmission eigenvalues is computed from a specific invariant ensemble for which explicit formula for the joint probability density of all eigenvalues is available. We revisit this problem in the large N regime allowing for (i) arbitrary ratio \U0001D719:=\U0001D441/\U0001D440≤1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit \U0001D719→0, we recover the formula for the density \U0001D70C that Beenakker (Rev Mod Phys 69:731–808, 1997) has derived for a special matrix ensemble. We also prove that the inverse square root singularity of the density at zero and full transmission in Beenakker’s formula persists for any \U0001D719<1 but in the borderline case \U0001D719=1 an anomalous \U0001D706−2/3 singularity arises at zero. To access this level of generality, we develop the theory of global and local laws on the spectral density of a large class of noncommutative rational expressions in large random matrices with i.i.d. entries." acknowledgement: The authors are very grateful to Yan Fyodorov for discussions on the physical background and for providing references, and to the anonymous referee for numerous valuable remarks. article_processing_charge: Yes (in subscription journal) article_type: original author: - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Torben H full_name: Krüger, Torben H id: 3020C786-F248-11E8-B48F-1D18A9856A87 last_name: Krüger orcid: 0000-0002-4821-3297 - first_name: Yuriy full_name: Nemish, Yuriy id: 4D902E6A-F248-11E8-B48F-1D18A9856A87 last_name: Nemish orcid: 0000-0002-7327-856X citation: ama: Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 2021;22:4205–4269. doi:10.1007/s00023-021-01085-6 apa: Erdös, L., Krüger, T. H., & Nemish, Y. (2021). Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . Springer Nature. https://doi.org/10.1007/s00023-021-01085-6 chicago: Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum Dots via Noncommutative Rational Functions.” Annales Henri Poincaré . Springer Nature, 2021. https://doi.org/10.1007/s00023-021-01085-6. ieee: L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative rational functions,” Annales Henri Poincaré , vol. 22. Springer Nature, pp. 4205–4269, 2021. ista: Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269. mla: Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational Functions.” Annales Henri Poincaré , vol. 22, Springer Nature, 2021, pp. 4205–4269, doi:10.1007/s00023-021-01085-6. short: L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré 22 (2021) 4205–4269. date_created: 2021-08-15T22:01:29Z date_published: 2021-12-01T00:00:00Z date_updated: 2023-08-11T10:31:48Z day: '01' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00023-021-01085-6 ec_funded: 1 external_id: arxiv: - '1911.05112' isi: - '000681531500001' file: - access_level: open_access checksum: 8d6bac0e2b0a28539608b0538a8e3b38 content_type: application/pdf creator: dernst date_created: 2022-05-12T12:50:27Z date_updated: 2022-05-12T12:50:27Z file_id: '11365' file_name: 2021_AnnHenriPoincare_Erdoes.pdf file_size: 1162454 relation: main_file success: 1 file_date_updated: 2022-05-12T12:50:27Z has_accepted_license: '1' intvolume: ' 22' isi: 1 language: - iso: eng month: '12' oa: 1 oa_version: Published Version page: 4205–4269 project: - _id: 258DCDE6-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '338804' name: Random matrices, universality and disordered quantum systems publication: 'Annales Henri Poincaré ' publication_identifier: eissn: - 1424-0661 issn: - 1424-0637 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Scattering in quantum dots via noncommutative rational functions tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 22 year: '2021' ... --- _id: '10221' abstract: - lang: eng text: We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020). acknowledgement: Open access funding provided by Institute of Science and Technology (IST Austria). article_processing_charge: Yes (via OA deal) article_type: original author: - first_name: Giorgio full_name: Cipolloni, Giorgio id: 42198EFA-F248-11E8-B48F-1D18A9856A87 last_name: Cipolloni orcid: 0000-0002-4901-7992 - first_name: László full_name: Erdös, László id: 4DBD5372-F248-11E8-B48F-1D18A9856A87 last_name: Erdös orcid: 0000-0001-5366-9603 - first_name: Dominik J full_name: Schröder, Dominik J id: 408ED176-F248-11E8-B48F-1D18A9856A87 last_name: Schröder orcid: 0000-0002-2904-1856 citation: ama: Cipolloni G, Erdös L, Schröder DJ. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 2021;388(2):1005–1048. doi:10.1007/s00220-021-04239-z apa: Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04239-z chicago: Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” Communications in Mathematical Physics. Springer Nature, 2021. https://doi.org/10.1007/s00220-021-04239-z. ieee: G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis for Wigner matrices,” Communications in Mathematical Physics, vol. 388, no. 2. Springer Nature, pp. 1005–1048, 2021. ista: Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048. mla: Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” Communications in Mathematical Physics, vol. 388, no. 2, Springer Nature, 2021, pp. 1005–1048, doi:10.1007/s00220-021-04239-z. short: G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048. date_created: 2021-11-07T23:01:25Z date_published: 2021-10-29T00:00:00Z date_updated: 2023-08-14T10:29:49Z day: '29' ddc: - '510' department: - _id: LaEr doi: 10.1007/s00220-021-04239-z external_id: arxiv: - '2012.13215' isi: - '000712232700001' file: - access_level: open_access checksum: a2c7b6f5d23b5453cd70d1261272283b content_type: application/pdf creator: cchlebak date_created: 2022-02-02T10:19:55Z date_updated: 2022-02-02T10:19:55Z file_id: '10715' file_name: 2021_CommunMathPhys_Cipolloni.pdf file_size: 841426 relation: main_file success: 1 file_date_updated: 2022-02-02T10:19:55Z has_accepted_license: '1' intvolume: ' 388' isi: 1 issue: '2' language: - iso: eng month: '10' oa: 1 oa_version: Published Version page: 1005–1048 project: - _id: B67AFEDC-15C9-11EA-A837-991A96BB2854 name: IST Austria Open Access Fund publication: Communications in Mathematical Physics publication_identifier: eissn: - 1432-0916 issn: - 0010-3616 publication_status: published publisher: Springer Nature quality_controlled: '1' scopus_import: '1' status: public title: Eigenstate thermalization hypothesis for Wigner matrices tmp: image: /images/cc_by.png legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0) short: CC BY (4.0) type: journal_article user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8 volume: 388 year: '2021' ...