[{"author":[{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137","first_name":"Guillaume","full_name":"Dubach, Guillaume","last_name":"Dubach"},{"last_name":"Mühlböck","full_name":"Mühlböck, Fabian","first_name":"Fabian","orcid":"0000-0003-1548-0177","id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425"}],"publication":"arXiv","date_published":"2021-03-21T00:00:00Z","department":[{"_id":"LaEr"},{"_id":"ToHe"}],"oa_version":"Preprint","external_id":{"arxiv":["2103.11389"]},"type":"preprint","title":"Formal verification of Zagier's one-sentence proof","oa":1,"related_material":{"record":[{"id":"9946","relation":"other","status":"public"}]},"publication_status":"submitted","arxiv":1,"language":[{"iso":"eng"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"9281","month":"03","doi":"10.48550/arXiv.2103.11389","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.11389"}],"citation":{"ama":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2103.11389\">10.48550/arXiv.2103.11389</a>","short":"G. Dubach, F. Mühlböck, ArXiv (n.d.).","mla":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” <i>ArXiv</i>, 2103.11389, doi:<a href=\"https://doi.org/10.48550/arXiv.2103.11389\">10.48550/arXiv.2103.11389</a>.","ieee":"G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,” <i>arXiv</i>. .","chicago":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2103.11389\">https://doi.org/10.48550/arXiv.2103.11389</a>.","apa":"Dubach, G., &#38; Mühlböck, F. (n.d.). Formal verification of Zagier’s one-sentence proof. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2103.11389\">https://doi.org/10.48550/arXiv.2103.11389</a>","ista":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv, 2103.11389."},"article_processing_charge":"No","day":"21","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"}],"article_number":"2103.11389","status":"public","ec_funded":1,"date_updated":"2023-05-03T10:26:45Z","project":[{"call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"year":"2021","date_created":"2021-03-23T05:38:48Z"},{"type":"journal_article","arxiv":1,"language":[{"iso":"eng"}],"publisher":"Mathematical Sciences Publishers","doi":"10.2140/pmp.2021.2.221","author":[{"last_name":"Alt","first_name":"Johannes","full_name":"Alt, Johannes","id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"publication":"Probability and Mathematical Physics","issue":"2","date_published":"2021-05-21T00:00:00Z","external_id":{"arxiv":["1907.13631"]},"oa_version":"Preprint","volume":2,"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"date_updated":"2024-02-19T08:30:00Z","year":"2021","date_created":"2024-02-18T23:01:03Z","quality_controlled":"1","page":"221-280","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1907.13631","open_access":"1"}],"scopus_import":"1","publication_identifier":{"eissn":["2690-1005"],"issn":["2690-0998"]},"article_processing_charge":"No","article_type":"original","publication_status":"published","oa":1,"title":"Spectral radius of random matrices with independent entries","_id":"15013","month":"05","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"acknowledgement":"Partially supported by ERC Starting Grant RandMat No. 715539 and the SwissMap grant of Swiss National Science Foundation. Partially supported by ERC Advanced Grant RanMat No. 338804. Partially supported by the Hausdorff Center for Mathematics in Bonn.","abstract":[{"lang":"eng","text":"We consider random n×n matrices X with independent and centered entries and a general variance profile. We show that the spectral radius of X converges with very high probability to the square root of the spectral radius of the variance matrix of X when n tends to infinity. We also establish the optimal rate of convergence, that is a new result even for general i.i.d. matrices beyond the explicitly solvable Gaussian cases. The main ingredient is the proof of the local inhomogeneous circular law [arXiv:1612.07776] at the spectral edge."}],"status":"public","ec_funded":1,"intvolume":"         2","citation":{"ama":"Alt J, Erdös L, Krüger TH. Spectral radius of random matrices with independent entries. <i>Probability and Mathematical Physics</i>. 2021;2(2):221-280. doi:<a href=\"https://doi.org/10.2140/pmp.2021.2.221\">10.2140/pmp.2021.2.221</a>","short":"J. Alt, L. Erdös, T.H. Krüger, Probability and Mathematical Physics 2 (2021) 221–280.","ieee":"J. Alt, L. Erdös, and T. H. Krüger, “Spectral radius of random matrices with independent entries,” <i>Probability and Mathematical Physics</i>, vol. 2, no. 2. Mathematical Sciences Publishers, pp. 221–280, 2021.","mla":"Alt, Johannes, et al. “Spectral Radius of Random Matrices with Independent Entries.” <i>Probability and Mathematical Physics</i>, vol. 2, no. 2, Mathematical Sciences Publishers, 2021, pp. 221–80, doi:<a href=\"https://doi.org/10.2140/pmp.2021.2.221\">10.2140/pmp.2021.2.221</a>.","apa":"Alt, J., Erdös, L., &#38; Krüger, T. H. (2021). Spectral radius of random matrices with independent entries. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2021.2.221\">https://doi.org/10.2140/pmp.2021.2.221</a>","ista":"Alt J, Erdös L, Krüger TH. 2021. Spectral radius of random matrices with independent entries. Probability and Mathematical Physics. 2(2), 221–280.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “Spectral Radius of Random Matrices with Independent Entries.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2021. <a href=\"https://doi.org/10.2140/pmp.2021.2.221\">https://doi.org/10.2140/pmp.2021.2.221</a>."},"day":"21"},{"status":"public","abstract":[{"text":"We prove that any deterministic matrix is approximately the identity in the eigenbasis of a large random Wigner matrix with very high probability and with an optimal error inversely proportional to the square root of the dimension. Our theorem thus rigorously verifies the Eigenstate Thermalisation Hypothesis by Deutsch (Phys Rev A 43:2046–2049, 1991) for the simplest chaotic quantum system, the Wigner ensemble. In mathematical terms, we prove the strong form of Quantum Unique Ergodicity (QUE) with an optimal convergence rate for all eigenvectors simultaneously, generalizing previous probabilistic QUE results in Bourgade and Yau (Commun Math Phys 350:231–278, 2017) and Bourgade et al. (Commun Pure Appl Math 73:1526–1596, 2020).","lang":"eng"}],"citation":{"ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Eigenstate thermalization hypothesis for Wigner matrices,” <i>Communications in Mathematical Physics</i>, vol. 388, no. 2. Springer Nature, pp. 1005–1048, 2021.","mla":"Cipolloni, Giorgio, et al. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <i>Communications in Mathematical Physics</i>, vol. 388, no. 2, Springer Nature, 2021, pp. 1005–1048, doi:<a href=\"https://doi.org/10.1007/s00220-021-04239-z\">10.1007/s00220-021-04239-z</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Eigenstate thermalization hypothesis for Wigner matrices. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-021-04239-z\">https://doi.org/10.1007/s00220-021-04239-z</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Eigenstate Thermalization Hypothesis for Wigner Matrices.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00220-021-04239-z\">https://doi.org/10.1007/s00220-021-04239-z</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048.","ama":"Cipolloni G, Erdös L, Schröder DJ. Eigenstate thermalization hypothesis for Wigner matrices. <i>Communications in Mathematical Physics</i>. 2021;388(2):1005–1048. doi:<a href=\"https://doi.org/10.1007/s00220-021-04239-z\">10.1007/s00220-021-04239-z</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048."},"intvolume":"       388","day":"29","has_accepted_license":"1","oa":1,"title":"Eigenstate thermalization hypothesis for Wigner matrices","publication_status":"published","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","month":"10","_id":"10221","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","department":[{"_id":"LaEr"}],"volume":388,"file":[{"checksum":"a2c7b6f5d23b5453cd70d1261272283b","relation":"main_file","creator":"cchlebak","file_size":841426,"file_name":"2021_CommunMathPhys_Cipolloni.pdf","date_updated":"2022-02-02T10:19:55Z","access_level":"open_access","success":1,"content_type":"application/pdf","date_created":"2022-02-02T10:19:55Z","file_id":"10715"}],"isi":1,"quality_controlled":"1","page":"1005–1048","year":"2021","date_created":"2021-11-07T23:01:25Z","date_updated":"2023-08-14T10:29:49Z","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"arxiv":1,"file_date_updated":"2022-02-02T10:19:55Z","type":"journal_article","doi":"10.1007/s00220-021-04239-z","publisher":"Springer Nature","publication":"Communications in Mathematical Physics","issue":"2","ddc":["510"],"author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"}],"external_id":{"isi":["000712232700001"],"arxiv":["2012.13215"]},"oa_version":"Published Version","date_published":"2021-10-29T00:00:00Z"},{"date_published":"2021-09-28T00:00:00Z","oa_version":"Published Version","author":[{"full_name":"Dubach, Guillaume","first_name":"Guillaume","last_name":"Dubach","orcid":"0000-0001-6892-8137","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"}],"ddc":["519"],"publication":"Electronic Journal of Probability","publisher":"Institute of Mathematical Statistics","doi":"10.1214/21-EJP686","type":"journal_article","file_date_updated":"2021-11-15T10:10:17Z","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"No","scopus_import":"1","publication_identifier":{"eissn":["1083-6489"]},"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"date_updated":"2021-11-15T10:48:46Z","year":"2021","date_created":"2021-11-14T23:01:25Z","quality_controlled":"1","file":[{"file_name":"2021_ElecJournalProb_Dubach.pdf","date_updated":"2021-11-15T10:10:17Z","success":1,"access_level":"open_access","date_created":"2021-11-15T10:10:17Z","file_id":"10288","content_type":"application/pdf","checksum":"1c975afb31460277ce4d22b93538e5f9","relation":"main_file","creator":"cchlebak","file_size":735940}],"volume":26,"department":[{"_id":"LaEr"}],"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.","month":"09","_id":"10285","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","article_type":"original","publication_status":"published","title":"On eigenvector statistics in the spherical and truncated unitary ensembles","oa":1,"has_accepted_license":"1","day":"28","intvolume":"        26","citation":{"chicago":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2021. <a href=\"https://doi.org/10.1214/21-EJP686\">https://doi.org/10.1214/21-EJP686</a>.","ista":"Dubach G. 2021. On eigenvector statistics in the spherical and truncated unitary ensembles. Electronic Journal of Probability. 26, 124.","apa":"Dubach, G. (2021). On eigenvector statistics in the spherical and truncated unitary ensembles. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-EJP686\">https://doi.org/10.1214/21-EJP686</a>","mla":"Dubach, Guillaume. “On Eigenvector Statistics in the Spherical and Truncated Unitary Ensembles.” <i>Electronic Journal of Probability</i>, vol. 26, 124, Institute of Mathematical Statistics, 2021, doi:<a href=\"https://doi.org/10.1214/21-EJP686\">10.1214/21-EJP686</a>.","ieee":"G. Dubach, “On eigenvector statistics in the spherical and truncated unitary ensembles,” <i>Electronic Journal of Probability</i>, vol. 26. Institute of Mathematical Statistics, 2021.","short":"G. Dubach, Electronic Journal of Probability 26 (2021).","ama":"Dubach G. On eigenvector statistics in the spherical and truncated unitary ensembles. <i>Electronic Journal of Probability</i>. 2021;26. doi:<a href=\"https://doi.org/10.1214/21-EJP686\">10.1214/21-EJP686</a>"},"ec_funded":1,"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."}],"status":"public","article_number":"124"},{"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"No","publication_identifier":{"eissn":["10836489"]},"scopus_import":"1","quality_controlled":"1","date_created":"2021-05-23T22:01:44Z","year":"2021","date_updated":"2023-08-08T13:39:19Z","project":[{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"volume":26,"isi":1,"file":[{"file_name":"2021_EJP_Cipolloni.pdf","file_id":"9423","date_created":"2021-05-25T13:24:19Z","content_type":"application/pdf","success":1,"date_updated":"2021-05-25T13:24:19Z","access_level":"open_access","relation":"main_file","checksum":"864ab003ad4cffea783f65aa8c2ba69f","file_size":865148,"creator":"kschuh"}],"oa_version":"Published Version","external_id":{"isi":["000641855600001"],"arxiv":["2002.02438"]},"date_published":"2021-03-23T00:00:00Z","publication":"Electronic Journal of Probability","ddc":["510"],"author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","full_name":"Schröder, Dominik J","last_name":"Schröder"}],"doi":"10.1214/21-EJP591","publisher":"Institute of Mathematical Statistics","arxiv":1,"language":[{"iso":"eng"}],"file_date_updated":"2021-05-25T13:24:19Z","type":"journal_article","day":"23","has_accepted_license":"1","intvolume":"        26","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Fluctuation around the circular law for random matrices with real entries. <i>Electronic Journal of Probability</i>. 2021;26. doi:<a href=\"https://doi.org/10.1214/21-EJP591\">10.1214/21-EJP591</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Electronic Journal of Probability 26 (2021).","mla":"Cipolloni, Giorgio, et al. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” <i>Electronic Journal of Probability</i>, vol. 26, 24, Institute of Mathematical Statistics, 2021, doi:<a href=\"https://doi.org/10.1214/21-EJP591\">10.1214/21-EJP591</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Fluctuation around the circular law for random matrices with real entries,” <i>Electronic Journal of Probability</i>, 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.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Fluctuation around the circular law for random matrices with real entries. <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/21-EJP591\">https://doi.org/10.1214/21-EJP591</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Fluctuation around the Circular Law for Random Matrices with Real Entries.” <i>Electronic Journal of Probability</i>. Institute of Mathematical Statistics, 2021. <a href=\"https://doi.org/10.1214/21-EJP591\">https://doi.org/10.1214/21-EJP591</a>."},"ec_funded":1,"article_number":"24","status":"public","abstract":[{"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.","lang":"eng"}],"department":[{"_id":"LaEr"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"9412","month":"03","oa":1,"title":"Fluctuation around the circular law for random matrices with real entries","publication_status":"published"},{"has_accepted_license":"1","day":"27","intvolume":"         9","citation":{"short":"Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).","ama":"Bao Z, Erdös L, Schnelli K. Equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. 2021;9. doi:<a href=\"https://doi.org/10.1017/fms.2021.38\">10.1017/fms.2021.38</a>","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>. Cambridge University Press, 2021. <a href=\"https://doi.org/10.1017/fms.2021.38\">https://doi.org/10.1017/fms.2021.38</a>.","ista":"Bao Z, Erdös L, Schnelli K. 2021. Equipartition principle for Wigner matrices. Forum of Mathematics, Sigma. 9, e44.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2021). Equipartition principle for Wigner matrices. <i>Forum of Mathematics, Sigma</i>. Cambridge University Press. <a href=\"https://doi.org/10.1017/fms.2021.38\">https://doi.org/10.1017/fms.2021.38</a>","mla":"Bao, Zhigang, et al. “Equipartition Principle for Wigner Matrices.” <i>Forum of Mathematics, Sigma</i>, vol. 9, e44, Cambridge University Press, 2021, doi:<a href=\"https://doi.org/10.1017/fms.2021.38\">10.1017/fms.2021.38</a>.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Equipartition principle for Wigner matrices,” <i>Forum of Mathematics, Sigma</i>, vol. 9. Cambridge University Press, 2021."},"ec_funded":1,"abstract":[{"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. ","lang":"eng"}],"status":"public","article_number":"e44","department":[{"_id":"LaEr"}],"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","_id":"9550","month":"05","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_type":"original","publication_status":"published","title":"Equipartition principle for Wigner matrices","oa":1,"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"No","scopus_import":"1","publication_identifier":{"eissn":["20505094"]},"project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"date_updated":"2023-08-08T14:03:40Z","date_created":"2021-06-13T22:01:33Z","year":"2021","quality_controlled":"1","file":[{"file_size":483458,"creator":"cziletti","relation":"main_file","checksum":"47c986578de132200d41e6d391905519","content_type":"application/pdf","file_id":"9555","date_created":"2021-06-15T14:40:45Z","access_level":"open_access","date_updated":"2021-06-15T14:40:45Z","success":1,"file_name":"2021_ForumMath_Bao.pdf"}],"isi":1,"volume":9,"date_published":"2021-05-27T00:00:00Z","external_id":{"isi":["000654960800001"],"arxiv":["2008.07061"]},"oa_version":"Published Version","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","last_name":"Bao","full_name":"Bao, Zhigang","first_name":"Zhigang"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Schnelli","full_name":"Schnelli, Kevin","first_name":"Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-0954-3231"}],"ddc":["510"],"publication":"Forum of Mathematics, Sigma","publisher":"Cambridge University Press","doi":"10.1017/fms.2021.38","type":"journal_article","file_date_updated":"2021-06-15T14:40:45Z","language":[{"iso":"eng"}],"arxiv":1},{"citation":{"short":"L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré  22 (2021) 4205–4269.","ama":"Erdös L, Krüger TH, Nemish Y. Scattering in quantum dots via noncommutative rational functions. <i>Annales Henri Poincaré </i>. 2021;22:4205–4269. doi:<a href=\"https://doi.org/10.1007/s00023-021-01085-6\">10.1007/s00023-021-01085-6</a>","chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Scattering in Quantum Dots via Noncommutative Rational Functions.” <i>Annales Henri Poincaré </i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00023-021-01085-6\">https://doi.org/10.1007/s00023-021-01085-6</a>.","ista":"Erdös L, Krüger TH, Nemish Y. 2021. Scattering in quantum dots via noncommutative rational functions. Annales Henri Poincaré . 22, 4205–4269.","apa":"Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2021). Scattering in quantum dots via noncommutative rational functions. <i>Annales Henri Poincaré </i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00023-021-01085-6\">https://doi.org/10.1007/s00023-021-01085-6</a>","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Scattering in quantum dots via noncommutative rational functions,” <i>Annales Henri Poincaré </i>, vol. 22. Springer Nature, pp. 4205–4269, 2021.","mla":"Erdös, László, et al. “Scattering in Quantum Dots via Noncommutative Rational Functions.” <i>Annales Henri Poincaré </i>, vol. 22, Springer Nature, 2021, pp. 4205–4269, doi:<a href=\"https://doi.org/10.1007/s00023-021-01085-6\">10.1007/s00023-021-01085-6</a>."},"intvolume":"        22","day":"01","has_accepted_license":"1","status":"public","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 𝑁≪𝑀 channels, the density 𝜌 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 𝜙:=𝑁/𝑀≤1; and (ii) general distributions for the matrix elements of the Hamiltonian of the quantum dot. In the limit 𝜙→0, we recover the formula for the density 𝜌 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 𝜙<1 but in the borderline case 𝜙=1 an anomalous 𝜆−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."}],"ec_funded":1,"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.","department":[{"_id":"LaEr"}],"publication_status":"published","oa":1,"title":"Scattering in quantum dots via noncommutative rational functions","article_type":"original","month":"12","_id":"9912","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]},"scopus_import":"1","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"article_processing_charge":"Yes (in subscription journal)","file":[{"creator":"dernst","file_size":1162454,"checksum":"8d6bac0e2b0a28539608b0538a8e3b38","relation":"main_file","access_level":"open_access","success":1,"date_updated":"2022-05-12T12:50:27Z","date_created":"2022-05-12T12:50:27Z","file_id":"11365","content_type":"application/pdf","file_name":"2021_AnnHenriPoincare_Erdoes.pdf"}],"isi":1,"volume":22,"year":"2021","date_created":"2021-08-15T22:01:29Z","quality_controlled":"1","page":"4205–4269","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"date_updated":"2023-08-11T10:31:48Z","publication":"Annales Henri Poincaré ","author":[{"first_name":"László","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Nemish, Yuriy","first_name":"Yuriy","last_name":"Nemish","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87"}],"ddc":["510"],"external_id":{"arxiv":["1911.05112"],"isi":["000681531500001"]},"oa_version":"Published Version","date_published":"2021-12-01T00:00:00Z","arxiv":1,"language":[{"iso":"eng"}],"type":"journal_article","file_date_updated":"2022-05-12T12:50:27Z","doi":"10.1007/s00023-021-01085-6","publisher":"Springer Nature"},{"citation":{"short":"Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348.","ama":"Bao Z, Erdös L, Schnelli K. On the support of the free additive convolution. <i>Journal d’Analyse Mathematique</i>. 2020;142:323-348. doi:<a href=\"https://doi.org/10.1007/s11854-020-0135-2\">10.1007/s11854-020-0135-2</a>","ista":"Bao Z, Erdös L, Schnelli K. 2020. On the support of the free additive convolution. Journal d’Analyse Mathematique. 142, 323–348.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). On the support of the free additive convolution. <i>Journal d’Analyse Mathematique</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11854-020-0135-2\">https://doi.org/10.1007/s11854-020-0135-2</a>","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “On the Support of the Free Additive Convolution.” <i>Journal d’Analyse Mathematique</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11854-020-0135-2\">https://doi.org/10.1007/s11854-020-0135-2</a>.","mla":"Bao, Zhigang, et al. “On the Support of the Free Additive Convolution.” <i>Journal d’Analyse Mathematique</i>, vol. 142, Springer Nature, 2020, pp. 323–48, doi:<a href=\"https://doi.org/10.1007/s11854-020-0135-2\">10.1007/s11854-020-0135-2</a>.","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “On the support of the free additive convolution,” <i>Journal d’Analyse Mathematique</i>, vol. 142. Springer Nature, pp. 323–348, 2020."},"intvolume":"       142","day":"01","status":"public","abstract":[{"text":"We consider the free additive convolution of two probability measures μ and ν on the real line and show that μ ⊞ v is supported on a single interval if μ and ν each has single interval support. Moreover, the density of μ ⊞ ν is proven to vanish as a square root near the edges of its support if both μ and ν have power law behavior with exponents between −1 and 1 near their edges. In particular, these results show the ubiquity of the conditions in our recent work on optimal local law at the spectral edges for addition of random matrices [5].","lang":"eng"}],"ec_funded":1,"department":[{"_id":"LaEr"}],"acknowledgement":"Supported in part by Hong Kong RGC Grant ECS 26301517.\r\nSupported in part by ERC Advanced Grant RANMAT No. 338804.\r\nSupported in part by the Knut and Alice Wallenberg Foundation and the Swedish Research Council Grant VR-2017-05195.","publication_status":"published","title":"On the support of the free additive convolution","oa":1,"article_type":"original","_id":"9104","month":"11","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"eissn":["15658538"],"issn":["00217670"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.11199"}],"scopus_import":"1","article_processing_charge":"No","isi":1,"volume":142,"date_created":"2021-02-07T23:01:15Z","year":"2020","quality_controlled":"1","page":"323-348","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7"}],"date_updated":"2023-08-24T11:16:03Z","publication":"Journal d'Analyse Mathematique","author":[{"last_name":"Bao","first_name":"Zhigang","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603"},{"orcid":"0000-0003-0954-3231","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","full_name":"Schnelli, Kevin","first_name":"Kevin"}],"oa_version":"Preprint","external_id":{"isi":["000611879400008"],"arxiv":["1804.11199"]},"date_published":"2020-11-01T00:00:00Z","language":[{"iso":"eng"}],"arxiv":1,"type":"journal_article","doi":"10.1007/s11854-020-0135-2","publisher":"Springer Nature"},{"author":[{"last_name":"Geher","full_name":"Geher, Gyorgy Pal","first_name":"Gyorgy Pal"},{"last_name":"Titkos","first_name":"Tamas","full_name":"Titkos, Tamas"},{"first_name":"Daniel","full_name":"Virosztek, Daniel","last_name":"Virosztek","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"ddc":["515"],"issue":"8","publication":"Transactions of the American Mathematical Society","date_published":"2020-08-01T00:00:00Z","external_id":{"arxiv":["2002.00859"],"isi":["000551418100018"]},"oa_version":"Preprint","type":"journal_article","arxiv":1,"language":[{"iso":"eng"}],"publisher":"American Mathematical Society","doi":"10.1090/tran/8113","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.00859"}],"publication_identifier":{"issn":["00029947"],"eissn":["10886850"]},"article_processing_charge":"No","isi":1,"volume":373,"project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","grant_number":"846294","name":"Geometric study of Wasserstein spaces and free probability","call_identifier":"H2020"}],"date_updated":"2023-08-17T14:31:03Z","year":"2020","date_created":"2020-01-29T10:20:46Z","page":"5855-5883","quality_controlled":"1","department":[{"_id":"LaEr"}],"article_type":"original","publication_status":"published","title":"Isometric study of Wasserstein spaces - the real line","oa":1,"month":"08","_id":"7389","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","intvolume":"       373","citation":{"chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Isometric Study of Wasserstein Spaces - the Real Line.” <i>Transactions of the American Mathematical Society</i>. American Mathematical Society, 2020. <a href=\"https://doi.org/10.1090/tran/8113\">https://doi.org/10.1090/tran/8113</a>.","apa":"Geher, G. P., Titkos, T., &#38; Virosztek, D. (2020). Isometric study of Wasserstein spaces - the real line. <i>Transactions of the American Mathematical Society</i>. American Mathematical Society. <a href=\"https://doi.org/10.1090/tran/8113\">https://doi.org/10.1090/tran/8113</a>","ista":"Geher GP, Titkos T, Virosztek D. 2020. Isometric study of Wasserstein spaces - the real line. Transactions of the American Mathematical Society. 373(8), 5855–5883.","mla":"Geher, Gyorgy Pal, et al. “Isometric Study of Wasserstein Spaces - the Real Line.” <i>Transactions of the American Mathematical Society</i>, vol. 373, no. 8, American Mathematical Society, 2020, pp. 5855–83, doi:<a href=\"https://doi.org/10.1090/tran/8113\">10.1090/tran/8113</a>.","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Isometric study of Wasserstein spaces - the real line,” <i>Transactions of the American Mathematical Society</i>, vol. 373, no. 8. American Mathematical Society, pp. 5855–5883, 2020.","short":"G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society 373 (2020) 5855–5883.","ama":"Geher GP, Titkos T, Virosztek D. Isometric study of Wasserstein spaces - the real line. <i>Transactions of the American Mathematical Society</i>. 2020;373(8):5855-5883. doi:<a href=\"https://doi.org/10.1090/tran/8113\">10.1090/tran/8113</a>"},"keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"day":"01","abstract":[{"text":"Recently Kloeckner described the structure of the isometry group of the quadratic Wasserstein space W_2(R^n). It turned out that the case of the real line is exceptional in the sense that there exists an exotic isometry flow. Following this line of investigation, we compute Isom(W_p(R)), the isometry group of the Wasserstein space\r\nW_p(R) for all p \\in [1,\\infty) \\setminus {2}. We show that W_2(R) is also exceptional regarding the\r\nparameter p: W_p(R) is isometrically rigid if and only if p is not equal to 2. Regarding the underlying\r\nspace, we prove that the exceptionality of p = 2 disappears if we replace R by the compact\r\ninterval [0,1]. Surprisingly, in that case, W_p([0,1]) is isometrically rigid if and only if\r\np is not equal to 1. Moreover, W_1([0,1]) admits isometries that split mass, and Isom(W_1([0,1]))\r\ncannot be embedded into Isom(W_1(R)).","lang":"eng"}],"status":"public","ec_funded":1},{"intvolume":"       278","citation":{"ama":"Erdös L, Krüger TH, Nemish Y. Local laws for polynomials of Wigner matrices. <i>Journal of Functional Analysis</i>. 2020;278(12). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108507\">10.1016/j.jfa.2020.108507</a>","short":"L. Erdös, T.H. Krüger, Y. Nemish, Journal of Functional Analysis 278 (2020).","mla":"Erdös, László, et al. “Local Laws for Polynomials of Wigner Matrices.” <i>Journal of Functional Analysis</i>, vol. 278, no. 12, 108507, Elsevier, 2020, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108507\">10.1016/j.jfa.2020.108507</a>.","ieee":"L. Erdös, T. H. Krüger, and Y. Nemish, “Local laws for polynomials of Wigner matrices,” <i>Journal of Functional Analysis</i>, vol. 278, no. 12. Elsevier, 2020.","chicago":"Erdös, László, Torben H Krüger, and Yuriy Nemish. “Local Laws for Polynomials of Wigner Matrices.” <i>Journal of Functional Analysis</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jfa.2020.108507\">https://doi.org/10.1016/j.jfa.2020.108507</a>.","ista":"Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 278(12), 108507.","apa":"Erdös, L., Krüger, T. H., &#38; Nemish, Y. (2020). Local laws for polynomials of Wigner matrices. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2020.108507\">https://doi.org/10.1016/j.jfa.2020.108507</a>"},"day":"01","status":"public","article_number":"108507","abstract":[{"text":"We consider general self-adjoint polynomials in several independent random matrices whose entries are centered and have the same variance. We show that under certain conditions the local law holds up to the optimal scale, i.e., the eigenvalue density on scales just above the eigenvalue spacing follows the global density of states which is determined by free probability theory. We prove that these conditions hold for general homogeneous polynomials of degree two and for symmetrized products of independent matrices with i.i.d. entries, thus establishing the optimal bulk local law for these classes of ensembles. In particular, we generalize a similar result of Anderson for anticommutator. For more general polynomials our conditions are effectively checkable numerically.","lang":"eng"}],"ec_funded":1,"department":[{"_id":"LaEr"}],"acknowledgement":"The authors are grateful to Oskari Ajanki for his invaluable help at the initial stage of this project, to Serban Belinschi for useful discussions, to Alexander Tikhomirov for calling our attention to the model example in Section 6.2 and to the anonymous referee for suggesting to simplify certain proofs. Erdös: Partially funded by ERC Advanced Grant RANMAT No. 338804\r\n","publication_status":"published","title":"Local laws for polynomials of Wigner matrices","oa":1,"article_type":"original","_id":"7512","month":"07","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["00221236"],"eissn":["10960783"]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.11340"}],"scopus_import":"1","article_processing_charge":"No","isi":1,"volume":278,"year":"2020","date_created":"2020-02-23T23:00:36Z","quality_controlled":"1","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"date_updated":"2023-08-18T06:36:10Z","publication":"Journal of Functional Analysis","issue":"12","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","last_name":"Krüger","full_name":"Krüger, Torben H","first_name":"Torben H"},{"first_name":"Yuriy","full_name":"Nemish, Yuriy","last_name":"Nemish","orcid":"0000-0002-7327-856X","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000522798900001"],"arxiv":["1804.11340"]},"oa_version":"Preprint","date_published":"2020-07-01T00:00:00Z","arxiv":1,"language":[{"iso":"eng"}],"type":"journal_article","doi":"10.1016/j.jfa.2020.108507","publisher":"Elsevier"},{"day":"01","citation":{"chicago":"Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.” <i>Letters in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s11005-020-01282-0\">https://doi.org/10.1007/s11005-020-01282-0</a>.","ista":"Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 110(8), 2039–2052.","apa":"Pitrik, J., &#38; Virosztek, D. (2020). Quantum Hellinger distances revisited. <i>Letters in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s11005-020-01282-0\">https://doi.org/10.1007/s11005-020-01282-0</a>","mla":"Pitrik, Jozsef, and Daniel Virosztek. “Quantum Hellinger Distances Revisited.” <i>Letters in Mathematical Physics</i>, vol. 110, no. 8, Springer Nature, 2020, pp. 2039–52, doi:<a href=\"https://doi.org/10.1007/s11005-020-01282-0\">10.1007/s11005-020-01282-0</a>.","ieee":"J. Pitrik and D. Virosztek, “Quantum Hellinger distances revisited,” <i>Letters in Mathematical Physics</i>, vol. 110, no. 8. Springer Nature, pp. 2039–2052, 2020.","short":"J. Pitrik, D. Virosztek, Letters in Mathematical Physics 110 (2020) 2039–2052.","ama":"Pitrik J, Virosztek D. Quantum Hellinger distances revisited. <i>Letters in Mathematical Physics</i>. 2020;110(8):2039-2052. doi:<a href=\"https://doi.org/10.1007/s11005-020-01282-0\">10.1007/s11005-020-01282-0</a>"},"intvolume":"       110","ec_funded":1,"status":"public","abstract":[{"text":"This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger divergences that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to the family of maximal quantum f-divergences, and hence are jointly convex, and satisfy the data processing inequality. We derive a characterization of the barycenter of finitely many positive definite operators for these generalized quantum Hellinger divergences. We note that the characterization of the barycenter as the weighted multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true in the case of commuting operators, but it is not correct in the general case. ","lang":"eng"}],"department":[{"_id":"LaEr"}],"acknowledgement":"J. Pitrik was supported by the Hungarian Academy of Sciences Lendület-Momentum Grant for Quantum\r\nInformation Theory, No. 96 141, and by the Hungarian National Research, Development and Innovation\r\nOffice (NKFIH) via Grants Nos. K119442, K124152 and KH129601. D. Virosztek was supported by the\r\nISTFELLOW program of the Institute of Science and Technology Austria (Project Code IC1027FELL01),\r\nby the European Union’s Horizon 2020 research and innovation program under the Marie\r\nSklodowska-Curie Grant Agreement No. 846294, and partially supported by the Hungarian National\r\nResearch, Development and Innovation Office (NKFIH) via Grants Nos. K124152 and KH129601.\r\nWe are grateful to Milán Mosonyi for drawing our attention to Ref.’s [6,14,15,17,\r\n20,21], for comments on earlier versions of this paper, and for several discussions on the topic. We are\r\nalso grateful to Miklós Pálfia for several discussions; to László Erdös for his essential suggestions on the\r\nstructure and highlights of this paper, and for his comments on earlier versions; and to the anonymous\r\nreferee for his/her valuable comments and suggestions.","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"7618","month":"08","title":"Quantum Hellinger distances revisited","oa":1,"publication_status":"published","article_type":"original","article_processing_charge":"No","publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1903.10455","open_access":"1"}],"page":"2039-2052","quality_controlled":"1","date_created":"2020-03-25T15:57:48Z","year":"2020","date_updated":"2023-08-18T10:17:26Z","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","grant_number":"291734","name":"International IST Postdoc Fellowship Programme","call_identifier":"FP7"}],"volume":110,"isi":1,"oa_version":"Preprint","external_id":{"arxiv":["1903.10455"],"isi":["000551556000002"]},"date_published":"2020-08-01T00:00:00Z","publication":"Letters in Mathematical Physics","issue":"8","author":[{"first_name":"Jozsef","full_name":"Pitrik, Jozsef","last_name":"Pitrik"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511","last_name":"Virosztek","first_name":"Daniel","full_name":"Virosztek, Daniel"}],"doi":"10.1007/s11005-020-01282-0","publisher":"Springer Nature","arxiv":1,"language":[{"iso":"eng"}],"type":"journal_article"},{"intvolume":"         1","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. <i>Probability and Mathematical Physics</i>. 2020;1(1):101-146. doi:<a href=\"https://doi.org/10.2140/pmp.2020.1.101\">10.2140/pmp.2020.1.101</a>","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability and Mathematical Physics 1 (2020) 101–146.","mla":"Cipolloni, Giorgio, et al. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” <i>Probability and Mathematical Physics</i>, vol. 1, no. 1, Mathematical Sciences Publishers, 2020, pp. 101–46, doi:<a href=\"https://doi.org/10.2140/pmp.2020.1.101\">10.2140/pmp.2020.1.101</a>.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Optimal lower bound on the least singular value of the shifted Ginibre ensemble,” <i>Probability and Mathematical Physics</i>, vol. 1, no. 1. Mathematical Sciences Publishers, pp. 101–146, 2020.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2020. Optimal lower bound on the least singular value of the shifted Ginibre ensemble. Probability and Mathematical Physics. 1(1), 101–146.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2020). Optimal lower bound on the least singular value of the shifted Ginibre ensemble. <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/pmp.2020.1.101\">https://doi.org/10.2140/pmp.2020.1.101</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Optimal Lower Bound on the Least Singular Value of the Shifted Ginibre Ensemble.” <i>Probability and Mathematical Physics</i>. Mathematical Sciences Publishers, 2020. <a href=\"https://doi.org/10.2140/pmp.2020.1.101\">https://doi.org/10.2140/pmp.2020.1.101</a>."},"keyword":["General Medicine"],"day":"16","abstract":[{"lang":"eng","text":"We consider the least singular value of a large random matrix with real or complex i.i.d. Gaussian entries shifted by a constant z∈C. We prove an optimal lower tail estimate on this singular value in the critical regime where z is around the spectral edge, thus improving the classical bound of Sankar, Spielman and Teng (SIAM J. Matrix Anal. Appl. 28:2 (2006), 446–476) for the particular shift-perturbation in the edge regime. Lacking Brézin–Hikami formulas in the real case, we rely on the superbosonization formula (Comm. Math. Phys. 283:2 (2008), 343–395)."}],"status":"public","ec_funded":1,"acknowledgement":"Partially supported by ERC Advanced Grant No. 338804. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 66538","department":[{"_id":"LaEr"}],"article_type":"original","title":"Optimal lower bound on the least singular value of the shifted Ginibre ensemble","oa":1,"publication_status":"published","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"11","_id":"15063","scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1908.01653"}],"publication_identifier":{"issn":["2690-1005","2690-0998"]},"article_processing_charge":"No","volume":1,"date_updated":"2024-03-04T10:33:15Z","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7"},{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"quality_controlled":"1","page":"101-146","year":"2020","date_created":"2024-03-04T10:27:57Z","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"issue":"1","publication":"Probability and Mathematical Physics","date_published":"2020-11-16T00:00:00Z","external_id":{"arxiv":["1908.01653"]},"oa_version":"Preprint","type":"journal_article","language":[{"iso":"eng"}],"arxiv":1,"publisher":"Mathematical Sciences Publishers","doi":"10.2140/pmp.2020.1.101"},{"file":[{"date_updated":"2023-12-18T10:42:32Z","success":1,"access_level":"open_access","file_id":"14695","date_created":"2023-12-18T10:42:32Z","content_type":"application/pdf","file_name":"2020_DocumentaMathematica_Alt.pdf","creator":"dernst","file_size":1374708,"checksum":"12aacc1d63b852ff9a51c1f6b218d4a6","relation":"main_file"}],"volume":25,"year":"2020","date_created":"2023-12-18T10:37:43Z","quality_controlled":"1","page":"1421-1539","date_updated":"2023-12-18T10:46:09Z","publication_identifier":{"eissn":["1431-0643"],"issn":["1431-0635"]},"article_processing_charge":"Yes","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"language":[{"iso":"eng"}],"arxiv":1,"type":"journal_article","file_date_updated":"2023-12-18T10:42:32Z","doi":"10.4171/dm/780","publisher":"EMS Press","publication":"Documenta Mathematica","author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","first_name":"Johannes","full_name":"Alt, Johannes","last_name":"Alt"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","first_name":"László"},{"first_name":"Torben H","full_name":"Krüger, Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297"}],"ddc":["510"],"oa_version":"Published Version","external_id":{"arxiv":["1804.07752"]},"date_published":"2020-09-01T00:00:00Z","status":"public","abstract":[{"lang":"eng","text":"We study the unique solution m of the Dyson equation \\( -m(z)^{-1} = z\\1 - a + S[m(z)] \\) on a von Neumann algebra A with the constraint Imm≥0. Here, z lies in the complex upper half-plane, a is a self-adjoint element of A and S is a positivity-preserving linear operator on A. We show that m is the Stieltjes transform of a compactly supported A-valued measure on R. Under suitable assumptions, we establish that this measure has a uniformly 1/3-Hölder continuous density with respect to the Lebesgue measure, which is supported on finitely many intervals, called bands. In fact, the density is analytic inside the bands with a square-root growth at the edges and internal cubic root cusps whenever the gap between two bands vanishes. The shape of these singularities is universal and no other singularity may occur. We give a precise asymptotic description of m near the singular points. These asymptotics generalize the analysis at the regular edges given in the companion paper on the Tracy-Widom universality for the edge eigenvalue statistics for correlated random matrices [the first author et al., Ann. Probab. 48, No. 2, 963--1001 (2020; Zbl 1434.60017)] and they play a key role in the proof of the Pearcey universality at the cusp for Wigner-type matrices [G. Cipolloni et al., Pure Appl. Anal. 1, No. 4, 615--707 (2019; Zbl 07142203); the second author et al., Commun. Math. Phys. 378, No. 2, 1203--1278 (2020; Zbl 07236118)]. We also extend the finite dimensional band mass formula from [the first author et al., loc. cit.] to the von Neumann algebra setting by showing that the spectral mass of the bands is topologically rigid under deformations and we conclude that these masses are quantized in some important cases."}],"keyword":["General Mathematics"],"citation":{"ieee":"J. Alt, L. Erdös, and T. H. Krüger, “The Dyson equation with linear self-energy: Spectral bands, edges and cusps,” <i>Documenta Mathematica</i>, vol. 25. EMS Press, pp. 1421–1539, 2020.","mla":"Alt, Johannes, et al. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” <i>Documenta Mathematica</i>, vol. 25, EMS Press, 2020, pp. 1421–539, doi:<a href=\"https://doi.org/10.4171/dm/780\">10.4171/dm/780</a>.","chicago":"Alt, Johannes, László Erdös, and Torben H Krüger. “The Dyson Equation with Linear Self-Energy: Spectral Bands, Edges and Cusps.” <i>Documenta Mathematica</i>. EMS Press, 2020. <a href=\"https://doi.org/10.4171/dm/780\">https://doi.org/10.4171/dm/780</a>.","ista":"Alt J, Erdös L, Krüger TH. 2020. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. Documenta Mathematica. 25, 1421–1539.","apa":"Alt, J., Erdös, L., &#38; Krüger, T. H. (2020). The Dyson equation with linear self-energy: Spectral bands, edges and cusps. <i>Documenta Mathematica</i>. EMS Press. <a href=\"https://doi.org/10.4171/dm/780\">https://doi.org/10.4171/dm/780</a>","ama":"Alt J, Erdös L, Krüger TH. The Dyson equation with linear self-energy: Spectral bands, edges and cusps. <i>Documenta Mathematica</i>. 2020;25:1421-1539. doi:<a href=\"https://doi.org/10.4171/dm/780\">10.4171/dm/780</a>","short":"J. Alt, L. Erdös, T.H. Krüger, Documenta Mathematica 25 (2020) 1421–1539."},"intvolume":"        25","day":"01","has_accepted_license":"1","publication_status":"published","oa":1,"related_material":{"record":[{"id":"6183","status":"public","relation":"earlier_version"}]},"title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","article_type":"original","month":"09","_id":"14694","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}]},{"oa_version":"Preprint","external_id":{"arxiv":["1804.07744"],"isi":["000528269100013"]},"date_published":"2020-03-01T00:00:00Z","publication":"Annals of Probability","issue":"2","author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","full_name":"Alt, Johannes","first_name":"Johannes"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László","full_name":"Erdös, László"},{"orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","first_name":"Torben H","last_name":"Krüger"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","first_name":"Dominik J","orcid":"0000-0002-2904-1856","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"doi":"10.1214/19-AOP1379","publisher":"Institute of Mathematical Statistics","arxiv":1,"language":[{"iso":"eng"}],"type":"journal_article","article_processing_charge":"No","publication_identifier":{"issn":["0091-1798"]},"scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1804.07744","open_access":"1"}],"page":"963-1001","quality_controlled":"1","year":"2020","date_created":"2019-03-28T09:20:08Z","date_updated":"2024-02-22T14:34:33Z","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"volume":48,"isi":1,"department":[{"_id":"LaEr"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","month":"03","_id":"6184","title":"Correlated random matrices: Band rigidity and edge universality","related_material":{"record":[{"id":"149","relation":"dissertation_contains","status":"public"},{"id":"6179","relation":"dissertation_contains","status":"public"}]},"oa":1,"publication_status":"published","article_type":"original","day":"01","citation":{"apa":"Alt, J., Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2020). Correlated random matrices: Band rigidity and edge universality. <i>Annals of Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/19-AOP1379\">https://doi.org/10.1214/19-AOP1379</a>","chicago":"Alt, Johannes, László Erdös, Torben H Krüger, and Dominik J Schröder. “Correlated Random Matrices: Band Rigidity and Edge Universality.” <i>Annals of Probability</i>. Institute of Mathematical Statistics, 2020. <a href=\"https://doi.org/10.1214/19-AOP1379\">https://doi.org/10.1214/19-AOP1379</a>.","ista":"Alt J, Erdös L, Krüger TH, Schröder DJ. 2020. Correlated random matrices: Band rigidity and edge universality. Annals of Probability. 48(2), 963–1001.","mla":"Alt, Johannes, et al. “Correlated Random Matrices: Band Rigidity and Edge Universality.” <i>Annals of Probability</i>, vol. 48, no. 2, Institute of Mathematical Statistics, 2020, pp. 963–1001, doi:<a href=\"https://doi.org/10.1214/19-AOP1379\">10.1214/19-AOP1379</a>.","ieee":"J. Alt, L. Erdös, T. H. Krüger, and D. J. Schröder, “Correlated random matrices: Band rigidity and edge universality,” <i>Annals of Probability</i>, vol. 48, no. 2. Institute of Mathematical Statistics, pp. 963–1001, 2020.","short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001.","ama":"Alt J, Erdös L, Krüger TH, Schröder DJ. Correlated random matrices: Band rigidity and edge universality. <i>Annals of Probability</i>. 2020;48(2):963-1001. doi:<a href=\"https://doi.org/10.1214/19-AOP1379\">10.1214/19-AOP1379</a>"},"intvolume":"        48","ec_funded":1,"status":"public","abstract":[{"text":"We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.","lang":"eng"}]},{"article_processing_charge":"Yes (via OA deal)","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)"},"scopus_import":"1","publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"date_updated":"2023-09-07T12:54:12Z","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"page":"1203-1278","quality_controlled":"1","date_created":"2019-03-28T10:21:15Z","year":"2020","volume":378,"isi":1,"file":[{"file_name":"2020_CommMathPhysics_Erdoes.pdf","date_created":"2020-11-18T11:14:37Z","content_type":"application/pdf","file_id":"8771","access_level":"open_access","success":1,"date_updated":"2020-11-18T11:14:37Z","relation":"main_file","checksum":"c3a683e2afdcea27afa6880b01e53dc2","file_size":2904574,"creator":"dernst"}],"date_published":"2020-09-01T00:00:00Z","external_id":{"arxiv":["1809.03971"],"isi":["000529483000001"]},"oa_version":"Published Version","ddc":["530","510"],"author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","first_name":"László","full_name":"Erdös, László","last_name":"Erdös"},{"first_name":"Torben H","full_name":"Krüger, Torben H","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297"},{"full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder","id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856"}],"publication":"Communications in Mathematical Physics","publisher":"Springer Nature","doi":"10.1007/s00220-019-03657-4","file_date_updated":"2020-11-18T11:14:37Z","type":"journal_article","language":[{"iso":"eng"}],"arxiv":1,"has_accepted_license":"1","day":"01","intvolume":"       378","citation":{"mla":"Erdös, László, et al. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” <i>Communications in Mathematical Physics</i>, vol. 378, Springer Nature, 2020, pp. 1203–78, doi:<a href=\"https://doi.org/10.1007/s00220-019-03657-4\">10.1007/s00220-019-03657-4</a>.","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” <i>Communications in Mathematical Physics</i>, vol. 378. Springer Nature, pp. 1203–1278, 2020.","ista":"Erdös L, Krüger TH, Schröder DJ. 2020. Cusp universality for random matrices I: Local law and the complex Hermitian case. Communications in Mathematical Physics. 378, 1203–1278.","chicago":"Erdös, László, Torben H Krüger, and Dominik J Schröder. “Cusp Universality for Random Matrices I: Local Law and the Complex Hermitian Case.” <i>Communications in Mathematical Physics</i>. Springer Nature, 2020. <a href=\"https://doi.org/10.1007/s00220-019-03657-4\">https://doi.org/10.1007/s00220-019-03657-4</a>.","apa":"Erdös, L., Krüger, T. H., &#38; Schröder, D. J. (2020). Cusp universality for random matrices I: Local law and the complex Hermitian case. <i>Communications in Mathematical Physics</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00220-019-03657-4\">https://doi.org/10.1007/s00220-019-03657-4</a>","ama":"Erdös L, Krüger TH, Schröder DJ. Cusp universality for random matrices I: Local law and the complex Hermitian case. <i>Communications in Mathematical Physics</i>. 2020;378:1203-1278. doi:<a href=\"https://doi.org/10.1007/s00220-019-03657-4\">10.1007/s00220-019-03657-4</a>","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278."},"ec_funded":1,"abstract":[{"text":"For complex Wigner-type matrices, i.e. Hermitian random matrices with independent, not necessarily identically distributed entries above the diagonal, we show that at any cusp singularity of the limiting eigenvalue distribution the local eigenvalue statistics are universal and form a Pearcey process. Since the density of states typically exhibits only square root or cubic root cusp singularities, our work complements previous results on the bulk and edge universality and it thus completes the resolution of the Wigner–Dyson–Mehta universality conjecture for the last remaining universality type in the complex Hermitian class. Our analysis holds not only for exact cusps, but approximate cusps as well, where an extended Pearcey process emerges. As a main technical ingredient we prove an optimal local law at the cusp for both symmetry classes. This result is also the key input in the companion paper (Cipolloni et al. in Pure Appl Anal, 2018. arXiv:1811.04055) where the cusp universality for real symmetric Wigner-type matrices is proven. The novel cusp fluctuation mechanism is also essential for the recent results on the spectral radius of non-Hermitian random matrices (Alt et al. in Spectral radius of random matrices with independent entries, 2019. arXiv:1907.13631), and the non-Hermitian edge universality (Cipolloni et al. in Edge universality for non-Hermitian random matrices, 2019. arXiv:1908.00969).","lang":"eng"}],"status":"public","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to Johannes Alt for numerous discussions on the Dyson equation and for his invaluable help in adjusting [10] to the needs of the present work.","department":[{"_id":"LaEr"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6185","month":"09","article_type":"original","related_material":{"record":[{"id":"6179","relation":"dissertation_contains","status":"public"}]},"title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","oa":1,"publication_status":"published"},{"external_id":{"arxiv":["1806.08751"],"isi":["000547464400001"]},"oa_version":"Preprint","date_published":"2020-07-01T00:00:00Z","issue":"3","publication":"Random Matrices: Theory and Application","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","first_name":"László"}],"doi":"10.1142/S2010326320500069","publisher":"World Scientific Publishing","arxiv":1,"language":[{"iso":"eng"}],"type":"journal_article","article_processing_charge":"No","publication_identifier":{"eissn":["20103271"],"issn":["20103263"]},"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1806.08751"}],"quality_controlled":"1","year":"2020","date_created":"2019-05-26T21:59:14Z","date_updated":"2023-08-28T08:38:48Z","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"volume":9,"isi":1,"department":[{"_id":"LaEr"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"6488","month":"07","oa":1,"title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","publication_status":"published","article_type":"original","day":"01","intvolume":"         9","citation":{"ama":"Cipolloni G, Erdös L. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. <i>Random Matrices: Theory and Application</i>. 2020;9(3). doi:<a href=\"https://doi.org/10.1142/S2010326320500069\">10.1142/S2010326320500069</a>","short":"G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020).","mla":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices: Theory and Application</i>, vol. 9, no. 3, 2050006, World Scientific Publishing, 2020, doi:<a href=\"https://doi.org/10.1142/S2010326320500069\">10.1142/S2010326320500069</a>.","ieee":"G. Cipolloni and L. Erdös, “Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices,” <i>Random Matrices: Theory and Application</i>, vol. 9, no. 3. World Scientific Publishing, 2020.","ista":"Cipolloni G, Erdös L. 2020. Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. Random Matrices: Theory and Application. 9(3), 2050006.","chicago":"Cipolloni, Giorgio, and László Erdös. “Fluctuations for Differences of Linear Eigenvalue Statistics for Sample Covariance Matrices.” <i>Random Matrices: Theory and Application</i>. World Scientific Publishing, 2020. <a href=\"https://doi.org/10.1142/S2010326320500069\">https://doi.org/10.1142/S2010326320500069</a>.","apa":"Cipolloni, G., &#38; Erdös, L. (2020). Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices. <i>Random Matrices: Theory and Application</i>. World Scientific Publishing. <a href=\"https://doi.org/10.1142/S2010326320500069\">https://doi.org/10.1142/S2010326320500069</a>"},"ec_funded":1,"article_number":"2050006","status":"public","abstract":[{"text":"We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish.","lang":"eng"}]},{"volume":279,"isi":1,"quality_controlled":"1","date_created":"2022-03-18T10:18:59Z","year":"2020","date_updated":"2023-08-24T14:08:42Z","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7"}],"publication_identifier":{"issn":["0022-1236"]},"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1708.01597"}],"article_processing_charge":"No","language":[{"iso":"eng"}],"arxiv":1,"type":"journal_article","doi":"10.1016/j.jfa.2020.108639","publisher":"Elsevier","publication":"Journal of Functional Analysis","issue":"7","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-3036-1475","first_name":"Zhigang","full_name":"Bao, Zhigang","last_name":"Bao"},{"orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","full_name":"Erdös, László","first_name":"László","last_name":"Erdös"},{"last_name":"Schnelli","first_name":"Kevin","full_name":"Schnelli, Kevin"}],"external_id":{"isi":["000559623200009"],"arxiv":["1708.01597"]},"oa_version":"Preprint","date_published":"2020-10-15T00:00:00Z","article_number":"108639","status":"public","abstract":[{"lang":"eng","text":"We consider the sum of two large Hermitian matrices A and B with a Haar unitary conjugation bringing them into a general relative position. We prove that the eigenvalue density on the scale slightly above the local eigenvalue spacing is asymptotically given by the free additive convolution of the laws of A and B as the dimension of the matrix increases. This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu's theorem. Our previous works [4], [5] established these results in the bulk spectrum, the current paper completely settles the problem at the spectral edges provided they have the typical square-root behavior. The key element of our proof is to compensate the deterioration of the stability of the subordination equations by sharp error estimates that properly account for the local density near the edge. Our results also hold if the Haar unitary matrix is replaced by the Haar orthogonal matrix."}],"ec_funded":1,"keyword":["Analysis"],"intvolume":"       279","citation":{"short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020).","ama":"Bao Z, Erdös L, Schnelli K. Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. 2020;279(7). doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>","chicago":"Bao, Zhigang, László Erdös, and Kevin Schnelli. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>. Elsevier, 2020. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>.","ista":"Bao Z, Erdös L, Schnelli K. 2020. Spectral rigidity for addition of random matrices at the regular edge. Journal of Functional Analysis. 279(7), 108639.","apa":"Bao, Z., Erdös, L., &#38; Schnelli, K. (2020). Spectral rigidity for addition of random matrices at the regular edge. <i>Journal of Functional Analysis</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">https://doi.org/10.1016/j.jfa.2020.108639</a>","ieee":"Z. Bao, L. Erdös, and K. Schnelli, “Spectral rigidity for addition of random matrices at the regular edge,” <i>Journal of Functional Analysis</i>, vol. 279, no. 7. Elsevier, 2020.","mla":"Bao, Zhigang, et al. “Spectral Rigidity for Addition of Random Matrices at the Regular Edge.” <i>Journal of Functional Analysis</i>, vol. 279, no. 7, 108639, Elsevier, 2020, doi:<a href=\"https://doi.org/10.1016/j.jfa.2020.108639\">10.1016/j.jfa.2020.108639</a>."},"day":"15","oa":1,"title":"Spectral rigidity for addition of random matrices at the regular edge","publication_status":"published","article_type":"original","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","_id":"10862","month":"10","acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804.","department":[{"_id":"LaEr"}]},{"date_updated":"2021-01-12T08:11:33Z","page":"34-41","quality_controlled":"1","date_created":"2019-11-18T15:39:53Z","year":"2019","volume":2125,"abstract":[{"lang":"eng","text":"The aim of this short note is to expound one particular issue that was discussed during the talk [10] given at the symposium ”Researches on isometries as preserver problems and related topics” at Kyoto RIMS. That is,  the role of Dirac masses by  describing  the  isometry group of various metric spaces  of probability  measures.   This  article  is  of  survey  character,  and  it  does  not  contain  any  essentially  new results.From an isometric point of view, in some cases, metric spaces of measures are similar to C(K)-type function  spaces.   Similarity  means  here  that  their  isometries  are  driven  by  some  nice  transformations of  the  underlying  space.   Of  course,  it  depends  on  the  particular  choice  of  the  metric  how  nice  these transformations should be.  Sometimes, as we will see, being a homeomorphism is enough to generate an isometry.  But sometimes we need more:  the transformation must preserve the underlying distance as well.  Statements claiming that isometries in questions are necessarily induced by homeomorphisms are called Banach-Stone-type results, while results asserting that the underlying transformation is necessarily an isometry are termed as isometric rigidity results.As  Dirac  masses  can  be  considered  as  building  bricks  of  the  set  of  all  Borel  measures,  a  natural question arises:Is it enough to understand how an isometry acts on the set of Dirac masses?  Does this action extend uniquely to all measures?In what follows, we will thoroughly investigate this question."}],"status":"public","article_processing_charge":"No","day":"30","intvolume":"      2125","main_file_link":[{"open_access":"1","url":"http://www.kurims.kyoto-u.ac.jp/~kyodo/kokyuroku/contents/2125.html"}],"citation":{"mla":"Geher, Gyorgy Pal, et al. “Dirac Masses and Isometric Rigidity.” <i>Kyoto RIMS Kôkyûroku</i>, vol. 2125, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41.","ieee":"G. P. Geher, T. Titkos, and D. Virosztek, “Dirac masses and isometric rigidity,” in <i>Kyoto RIMS Kôkyûroku</i>, Kyoto, Japan, 2019, vol. 2125, pp. 34–41.","apa":"Geher, G. P., Titkos, T., &#38; Virosztek, D. (2019). Dirac masses and isometric rigidity. In <i>Kyoto RIMS Kôkyûroku</i> (Vol. 2125, pp. 34–41). Kyoto, Japan: Research Institute for Mathematical Sciences, Kyoto University.","ista":"Geher GP, Titkos T, Virosztek D. 2019. Dirac masses and isometric rigidity. Kyoto RIMS Kôkyûroku. Research on isometries as preserver problems and related topics vol. 2125, 34–41.","chicago":"Geher, Gyorgy Pal, Tamas Titkos, and Daniel Virosztek. “Dirac Masses and Isometric Rigidity.” In <i>Kyoto RIMS Kôkyûroku</i>, 2125:34–41. Research Institute for Mathematical Sciences, Kyoto University, 2019.","ama":"Geher GP, Titkos T, Virosztek D. Dirac masses and isometric rigidity. In: <i>Kyoto RIMS Kôkyûroku</i>. Vol 2125. Research Institute for Mathematical Sciences, Kyoto University; 2019:34-41.","short":"G.P. Geher, T. Titkos, D. Virosztek, in:, Kyoto RIMS Kôkyûroku, Research Institute for Mathematical Sciences, Kyoto University, 2019, pp. 34–41."},"publisher":"Research Institute for Mathematical Sciences, Kyoto University","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"01","_id":"7035","type":"conference","oa":1,"title":"Dirac masses and isometric rigidity","publication_status":"published","language":[{"iso":"eng"}],"date_published":"2019-01-30T00:00:00Z","department":[{"_id":"LaEr"}],"oa_version":"Submitted Version","conference":{"start_date":"2019-01-28","name":"Research on isometries as preserver problems and related topics","end_date":"2019-01-30","location":"Kyoto, Japan"},"author":[{"full_name":"Geher, Gyorgy Pal","first_name":"Gyorgy Pal","last_name":"Geher"},{"last_name":"Titkos","first_name":"Tamas","full_name":"Titkos, Tamas"},{"id":"48DB45DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","first_name":"Daniel","last_name":"Virosztek"}],"publication":"Kyoto RIMS Kôkyûroku"},{"article_processing_charge":"No","scopus_import":"1","main_file_link":[{"url":"https://arxiv.org/abs/1710.02323","open_access":"1"}],"publication_identifier":{"issn":["0246-0203"]},"date_updated":"2023-10-17T08:53:45Z","project":[{"call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"call_identifier":"H2020","_id":"256E75B8-B435-11E9-9278-68D0E5697425","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}],"quality_controlled":"1","page":"1203-1225","year":"2019","date_created":"2018-12-11T11:44:29Z","volume":55,"isi":1,"date_published":"2019-09-25T00:00:00Z","oa_version":"Preprint","external_id":{"arxiv":["1710.02323"],"isi":["000487763200001"]},"author":[{"last_name":"Ferrari","full_name":"Ferrari, Patrick","first_name":"Patrick"},{"last_name":"Ghosal","full_name":"Ghosal, Promit","first_name":"Promit"},{"first_name":"Peter","full_name":"Nejjar, Peter","last_name":"Nejjar","id":"4BF426E2-F248-11E8-B48F-1D18A9856A87"}],"publication":"Annales de l'institut Henri Poincare (B) Probability and Statistics","issue":"3","publisher":"Institute of Mathematical Statistics","doi":"10.1214/18-AIHP916","type":"journal_article","arxiv":1,"language":[{"iso":"eng"}],"day":"25","citation":{"ama":"Ferrari P, Ghosal P, Nejjar P. Limit law of a second class particle in TASEP with non-random initial condition. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. 2019;55(3):1203-1225. doi:<a href=\"https://doi.org/10.1214/18-AIHP916\">10.1214/18-AIHP916</a>","short":"P. Ferrari, P. Ghosal, P. Nejjar, Annales de l’institut Henri Poincare (B) Probability and Statistics 55 (2019) 1203–1225.","ieee":"P. Ferrari, P. Ghosal, and P. Nejjar, “Limit law of a second class particle in TASEP with non-random initial condition,” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 55, no. 3. Institute of Mathematical Statistics, pp. 1203–1225, 2019.","mla":"Ferrari, Patrick, et al. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>, vol. 55, no. 3, Institute of Mathematical Statistics, 2019, pp. 1203–25, doi:<a href=\"https://doi.org/10.1214/18-AIHP916\">10.1214/18-AIHP916</a>.","ista":"Ferrari P, Ghosal P, Nejjar P. 2019. Limit law of a second class particle in TASEP with non-random initial condition. Annales de l’institut Henri Poincare (B) Probability and Statistics. 55(3), 1203–1225.","chicago":"Ferrari, Patrick, Promit Ghosal, and Peter Nejjar. “Limit Law of a Second Class Particle in TASEP with Non-Random Initial Condition.” <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics, 2019. <a href=\"https://doi.org/10.1214/18-AIHP916\">https://doi.org/10.1214/18-AIHP916</a>.","apa":"Ferrari, P., Ghosal, P., &#38; Nejjar, P. (2019). Limit law of a second class particle in TASEP with non-random initial condition. <i>Annales de l’institut Henri Poincare (B) Probability and Statistics</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-AIHP916\">https://doi.org/10.1214/18-AIHP916</a>"},"intvolume":"        55","ec_funded":1,"abstract":[{"lang":"eng","text":"We consider the totally asymmetric simple exclusion process (TASEP) with non-random initial condition having density ρ on ℤ− and λ on ℤ+, and a second class particle initially at the origin. For ρ&lt;λ, there is a shock and the second class particle moves with speed 1−λ−ρ. For large time t, we show that the position of the second class particle fluctuates on a t1/3 scale and determine its limiting law. We also obtain the limiting distribution of the number of steps made by the second class particle until time t."}],"status":"public","department":[{"_id":"LaEr"},{"_id":"JaMa"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","_id":"72","month":"09","article_type":"original","title":"Limit law of a second class particle in TASEP with non-random initial condition","oa":1,"publication_status":"published"},{"department":[{"_id":"LaEr"}],"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","month":"02","_id":"7423","article_type":"original","title":"Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles","oa":1,"publication_status":"published","day":"01","citation":{"apa":"Akemann, G., Checinski, T., Liu, D., &#38; Strahov, E. (2019). Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/18-aihp888\">https://doi.org/10.1214/18-aihp888</a>","ista":"Akemann G, Checinski T, Liu D, Strahov E. 2019. Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. 55(1), 441–479.","chicago":"Akemann, Gernot, Tomasz Checinski, Dangzheng Liu, and Eugene Strahov. “Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated to Two Wishart Ensembles.” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. Institute of Mathematical Statistics, 2019. <a href=\"https://doi.org/10.1214/18-aihp888\">https://doi.org/10.1214/18-aihp888</a>.","mla":"Akemann, Gernot, et al. “Finite Rank Perturbations in Products of Coupled Random Matrices: From One Correlated to Two Wishart Ensembles.” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>, vol. 55, no. 1, Institute of Mathematical Statistics, 2019, pp. 441–79, doi:<a href=\"https://doi.org/10.1214/18-aihp888\">10.1214/18-aihp888</a>.","ieee":"G. Akemann, T. Checinski, D. Liu, and E. Strahov, “Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles,” <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>, vol. 55, no. 1. Institute of Mathematical Statistics, pp. 441–479, 2019.","short":"G. Akemann, T. Checinski, D. Liu, E. Strahov, Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 55 (2019) 441–479.","ama":"Akemann G, Checinski T, Liu D, Strahov E. Finite rank perturbations in products of coupled random matrices: From one correlated to two Wishart ensembles. <i>Annales de l’Institut Henri Poincaré, Probabilités et Statistiques</i>. 2019;55(1):441-479. doi:<a href=\"https://doi.org/10.1214/18-aihp888\">10.1214/18-aihp888</a>"},"intvolume":"        55","abstract":[{"lang":"eng","text":"We compare finite rank perturbations of the following three ensembles of complex rectangular random matrices: First, a generalised Wishart ensemble with one random and two fixed correlation matrices introduced by Borodin and Péché, second, the product of two independent random matrices where one has correlated entries, and third, the case when the two random matrices become also coupled through a fixed matrix. The singular value statistics of all three ensembles is shown to be determinantal and we derive double contour integral representations for their respective kernels. Three different kernels are found in the limit of infinite matrix dimension at the origin of the spectrum. They depend on finite rank perturbations of the correlation and coupling matrices and are shown to be integrable. The first kernel (I) is found for two independent matrices from the second, and two weakly coupled matrices from the third ensemble. It generalises the Meijer G-kernel for two independent and uncorrelated matrices. The third kernel (III) is obtained for the generalised Wishart ensemble and for two strongly coupled matrices. It further generalises the perturbed Bessel kernel of Desrosiers and Forrester. Finally, kernel (II), found for the ensemble of two coupled matrices, provides an interpolation between the kernels (I) and (III), generalising previous findings of part of the authors."}],"status":"public","date_published":"2019-02-01T00:00:00Z","oa_version":"Preprint","external_id":{"isi":["000456070200013"],"arxiv":["1704.05224"]},"author":[{"last_name":"Akemann","full_name":"Akemann, Gernot","first_name":"Gernot"},{"full_name":"Checinski, Tomasz","first_name":"Tomasz","last_name":"Checinski"},{"first_name":"Dangzheng","full_name":"Liu, Dangzheng","last_name":"Liu","id":"2F947E34-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Strahov","first_name":"Eugene","full_name":"Strahov, Eugene"}],"publication":"Annales de l'Institut Henri Poincaré, Probabilités et Statistiques","issue":"1","publisher":"Institute of Mathematical Statistics","doi":"10.1214/18-aihp888","type":"journal_article","arxiv":1,"language":[{"iso":"eng"}],"article_processing_charge":"No","main_file_link":[{"url":"https://arxiv.org/abs/1704.05224","open_access":"1"}],"publication_identifier":{"issn":["0246-0203"]},"date_updated":"2023-09-06T14:58:39Z","quality_controlled":"1","page":"441-479","year":"2019","date_created":"2020-01-30T10:36:50Z","volume":55,"isi":1}]