[{"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."}],"oa":1,"arxiv":1,"doi":"10.48550/arXiv.2103.04817","day":"08","date_published":"2021-03-08T00:00:00Z","external_id":{"arxiv":["2103.04817"]},"type":"preprint","date_updated":"2023-05-03T10:22:59Z","citation":{"short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).","mla":"Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” <i>ArXiv</i>, 2103.04817, doi:<a href=\"https://doi.org/10.48550/arXiv.2103.04817\">10.48550/arXiv.2103.04817</a>.","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.","ama":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. <i>arXiv</i>. doi:<a href=\"https://doi.org/10.48550/arXiv.2103.04817\">10.48550/arXiv.2103.04817</a>","apa":"Arguin, L.-P., Dubach, G., &#38; Hartung, L. (n.d.). Maxima of a random model of the Riemann zeta function over intervals of varying length. <i>arXiv</i>. <a href=\"https://doi.org/10.48550/arXiv.2103.04817\">https://doi.org/10.48550/arXiv.2103.04817</a>","ieee":"L.-P. Arguin, G. Dubach, and L. Hartung, “Maxima of a random model of the Riemann zeta function over intervals of varying length,” <i>arXiv</i>. .","chicago":"Arguin, Louis-Pierre, Guillaume Dubach, and Lisa Hartung. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” <i>ArXiv</i>, n.d. <a href=\"https://doi.org/10.48550/arXiv.2103.04817\">https://doi.org/10.48550/arXiv.2103.04817</a>."},"year":"2021","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","acknowledgement":"The research of L.-P. A. is supported in part by the grant NSF CAREER DMS-1653602. G. D. gratefully acknowledges support from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. The research of L. H. is supported in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through Project-ID 233630050 -TRR 146, Project-ID 443891315 within SPP 2265 and Project-ID 446173099.","main_file_link":[{"url":"https://arxiv.org/abs/2103.04817","open_access":"1"}],"title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","month":"03","article_number":"2103.04817","publication_status":"submitted","oa_version":"Preprint","project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"article_processing_charge":"No","date_created":"2021-03-09T11:08:15Z","department":[{"_id":"LaEr"}],"author":[{"last_name":"Arguin","first_name":"Louis-Pierre","full_name":"Arguin, Louis-Pierre"},{"orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","first_name":"Guillaume","last_name":"Dubach","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E"},{"full_name":"Hartung, Lisa","last_name":"Hartung","first_name":"Lisa"}],"_id":"9230","publication":"arXiv","language":[{"iso":"eng"}],"ec_funded":1},{"language":[{"iso":"eng"}],"ec_funded":1,"month":"03","title":"Formal verification of Zagier's one-sentence proof","article_number":"2103.11389","publication_status":"submitted","oa_version":"Preprint","department":[{"_id":"LaEr"},{"_id":"ToHe"}],"article_processing_charge":"No","project":[{"_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"date_created":"2021-03-23T05:38:48Z","author":[{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","first_name":"Guillaume","last_name":"Dubach"},{"full_name":"Mühlböck, Fabian","orcid":"0000-0003-1548-0177","last_name":"Mühlböck","first_name":"Fabian","id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425"}],"_id":"9281","publication":"arXiv","status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"relation":"other","id":"9946","status":"public"}]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2103.11389"}],"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"}],"oa":1,"arxiv":1,"doi":"10.48550/arXiv.2103.11389","day":"21","date_published":"2021-03-21T00:00:00Z","type":"preprint","external_id":{"arxiv":["2103.11389"]},"date_updated":"2023-05-03T10:26:45Z","citation":{"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>.","ieee":"G. Dubach and F. Mühlböck, “Formal verification of Zagier’s one-sentence proof,” <i>arXiv</i>. .","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>","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.","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>."},"year":"2021"},{"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","file":[{"file_size":865148,"checksum":"864ab003ad4cffea783f65aa8c2ba69f","date_created":"2021-05-25T13:24:19Z","file_name":"2021_EJP_Cipolloni.pdf","content_type":"application/pdf","date_updated":"2021-05-25T13:24:19Z","success":1,"access_level":"open_access","relation":"main_file","creator":"kschuh","file_id":"9423"}],"oa":1,"publication_identifier":{"eissn":["10836489"]},"type":"journal_article","date_published":"2021-03-23T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"language":[{"iso":"eng"}],"article_number":"24","month":"03","project":[{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"oa_version":"Published Version","has_accepted_license":"1","publication":"Electronic Journal of Probability","ddc":["510"],"volume":26,"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"}],"day":"23","arxiv":1,"doi":"10.1214/21-EJP591","external_id":{"isi":["000641855600001"],"arxiv":["2002.02438"]},"isi":1,"citation":{"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>.","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.","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>","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>","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.","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>."},"year":"2021","date_updated":"2023-08-08T13:39:19Z","publisher":"Institute of Mathematical Statistics","file_date_updated":"2021-05-25T13:24:19Z","quality_controlled":"1","ec_funded":1,"intvolume":"        26","title":"Fluctuation around the circular law for random matrices with real entries","date_created":"2021-05-23T22:01:44Z","article_processing_charge":"No","department":[{"_id":"LaEr"}],"publication_status":"published","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"9412"},{"oa":1,"publication_identifier":{"eissn":["20505094"]},"type":"journal_article","date_published":"2021-05-27T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"date_created":"2021-06-15T14:40:45Z","file_size":483458,"checksum":"47c986578de132200d41e6d391905519","date_updated":"2021-06-15T14:40:45Z","file_name":"2021_ForumMath_Bao.pdf","content_type":"application/pdf","access_level":"open_access","relation":"main_file","success":1,"file_id":"9555","creator":"cziletti"}],"article_number":"e44","month":"05","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"}],"oa_version":"Published Version","has_accepted_license":"1","publication":"Forum of Mathematics, Sigma","language":[{"iso":"eng"}],"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"}],"day":"27","arxiv":1,"doi":"10.1017/fms.2021.38","external_id":{"arxiv":["2008.07061"],"isi":["000654960800001"]},"isi":1,"citation":{"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.” <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>.","short":"Z. Bao, L. Erdös, K. Schnelli, Forum of Mathematics, Sigma 9 (2021).","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.","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>.","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>","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>"},"year":"2021","date_updated":"2023-08-08T14:03:40Z","ddc":["510"],"volume":9,"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","intvolume":"         9","title":"Equipartition principle for Wigner matrices","department":[{"_id":"LaEr"}],"date_created":"2021-06-13T22:01:33Z","article_processing_charge":"No","publication_status":"published","author":[{"first_name":"Zhigang","last_name":"Bao","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Kevin","last_name":"Schnelli","orcid":"0000-0003-0954-3231","full_name":"Schnelli, Kevin","id":"434AD0AE-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"9550","article_type":"original","publisher":"Cambridge University Press","file_date_updated":"2021-06-15T14:40:45Z","quality_controlled":"1","ec_funded":1},{"language":[{"iso":"eng"}],"month":"10","oa_version":"Published Version","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publication":"Communications in Mathematical Physics","has_accepted_license":"1","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","file":[{"date_created":"2022-02-02T10:19:55Z","checksum":"a2c7b6f5d23b5453cd70d1261272283b","file_size":841426,"date_updated":"2022-02-02T10:19:55Z","file_name":"2021_CommunMathPhys_Cipolloni.pdf","content_type":"application/pdf","access_level":"open_access","success":1,"relation":"main_file","file_id":"10715","creator":"cchlebak"}],"oa":1,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"date_published":"2021-10-29T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"article_type":"original","publisher":"Springer Nature","file_date_updated":"2022-02-02T10:19:55Z","page":"1005–1048","quality_controlled":"1","title":"Eigenstate thermalization hypothesis for Wigner matrices","intvolume":"       388","publication_status":"published","date_created":"2021-11-07T23:01:25Z","department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J"}],"issue":"2","_id":"10221","scopus_import":"1","ddc":["510"],"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).","volume":388,"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"}],"doi":"10.1007/s00220-021-04239-z","arxiv":1,"day":"29","isi":1,"external_id":{"arxiv":["2012.13215"],"isi":["000712232700001"]},"date_updated":"2023-08-14T10:29:49Z","citation":{"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>","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>","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.","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>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Communications in Mathematical Physics 388 (2021) 1005–1048.","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>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Eigenstate thermalization hypothesis for Wigner matrices. Communications in Mathematical Physics. 388(2), 1005–1048."},"year":"2021"},{"_id":"10285","scopus_import":"1","author":[{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","last_name":"Dubach","first_name":"Guillaume","full_name":"Dubach, Guillaume","orcid":"0000-0001-6892-8137"}],"publication_status":"published","date_created":"2021-11-14T23:01:25Z","article_processing_charge":"No","department":[{"_id":"LaEr"}],"title":"On eigenvector statistics in the spherical and truncated unitary ensembles","intvolume":"        26","ec_funded":1,"quality_controlled":"1","file_date_updated":"2021-11-15T10:10:17Z","publisher":"Institute of Mathematical Statistics","article_type":"original","date_updated":"2021-11-15T10:48:46Z","citation":{"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.","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>.","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>","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>","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.” <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>.","short":"G. Dubach, Electronic Journal of Probability 26 (2021)."},"year":"2021","doi":"10.1214/21-EJP686","day":"28","abstract":[{"text":"We study the overlaps between right and left eigenvectors for random matrices of the spherical ensemble, as well as truncated unitary ensembles in the regime where half of the matrix at least is truncated. These two integrable models exhibit a form of duality, and the essential steps of our investigation can therefore be performed in parallel. In every case, conditionally on all eigenvalues, diagonal overlaps are shown to be distributed as a product of independent random variables with explicit distributions. This enables us to prove that the scaled diagonal overlaps, conditionally on one eigenvalue, converge in distribution to a heavy-tail limit, namely, the inverse of a γ2 distribution. We also provide formulae for the conditional expectation of diagonal and off-diagonal overlaps, either with respect to one eigenvalue, or with respect to the whole spectrum. These results, analogous to what is known for the complex Ginibre ensemble, can be obtained in these cases thanks to integration techniques inspired from a previous work by Forrester & Krishnapur.","lang":"eng"}],"volume":26,"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.","ddc":["519"],"publication":"Electronic Journal of Probability","has_accepted_license":"1","oa_version":"Published Version","project":[{"name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"month":"09","article_number":"124","language":[{"iso":"eng"}],"tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"date_published":"2021-09-28T00:00:00Z","type":"journal_article","publication_identifier":{"eissn":["1083-6489"]},"oa":1,"file":[{"file_size":735940,"checksum":"1c975afb31460277ce4d22b93538e5f9","date_created":"2021-11-15T10:10:17Z","file_name":"2021_ElecJournalProb_Dubach.pdf","content_type":"application/pdf","date_updated":"2021-11-15T10:10:17Z","access_level":"open_access","relation":"main_file","success":1,"creator":"cchlebak","file_id":"10288"}],"user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9","status":"public"},{"file_date_updated":"2022-05-12T12:50:27Z","quality_controlled":"1","ec_funded":1,"page":"4205–4269","article_type":"original","publisher":"Springer Nature","author":[{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"},{"first_name":"Yuriy","last_name":"Nemish","orcid":"0000-0002-7327-856X","full_name":"Nemish, Yuriy","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87"}],"scopus_import":"1","_id":"9912","intvolume":"        22","title":"Scattering in quantum dots via noncommutative rational functions","article_processing_charge":"Yes (in subscription journal)","date_created":"2021-08-15T22:01:29Z","department":[{"_id":"LaEr"}],"publication_status":"published","ddc":["510"],"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.","volume":22,"external_id":{"isi":["000681531500001"],"arxiv":["1911.05112"]},"isi":1,"year":"2021","citation":{"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.” <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>.","short":"L. Erdös, T.H. Krüger, Y. Nemish, Annales Henri Poincaré  22 (2021) 4205–4269.","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.","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>.","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>","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>"},"date_updated":"2023-08-11T10:31:48Z","abstract":[{"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.","lang":"eng"}],"day":"01","doi":"10.1007/s00023-021-01085-6","arxiv":1,"language":[{"iso":"eng"}],"has_accepted_license":"1","publication":"Annales Henri Poincaré ","month":"12","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"oa_version":"Published Version","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","file":[{"checksum":"8d6bac0e2b0a28539608b0538a8e3b38","file_size":1162454,"date_created":"2022-05-12T12:50:27Z","file_name":"2021_AnnHenriPoincare_Erdoes.pdf","content_type":"application/pdf","date_updated":"2022-05-12T12:50:27Z","access_level":"open_access","relation":"main_file","success":1,"creator":"dernst","file_id":"11365"}],"type":"journal_article","date_published":"2021-12-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"oa":1,"publication_identifier":{"eissn":["1424-0661"],"issn":["1424-0637"]}},{"month":"10","article_number":"108639","oa_version":"Preprint","project":[{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"publication":"Journal of Functional Analysis","language":[{"iso":"eng"}],"keyword":["Analysis"],"oa":1,"publication_identifier":{"issn":["0022-1236"]},"date_published":"2020-10-15T00:00:00Z","type":"journal_article","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","main_file_link":[{"url":"https://arxiv.org/abs/1708.01597","open_access":"1"}],"title":"Spectral rigidity for addition of random matrices at the regular edge","intvolume":"       279","publication_status":"published","article_processing_charge":"No","department":[{"_id":"LaEr"}],"date_created":"2022-03-18T10:18:59Z","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","first_name":"Zhigang"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Schnelli","first_name":"Kevin","full_name":"Schnelli, Kevin"}],"issue":"7","_id":"10862","scopus_import":"1","article_type":"original","publisher":"Elsevier","quality_controlled":"1","ec_funded":1,"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."}],"doi":"10.1016/j.jfa.2020.108639","arxiv":1,"day":"15","isi":1,"external_id":{"arxiv":["1708.01597"],"isi":["000559623200009"]},"date_updated":"2023-08-24T14:08:42Z","citation":{"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.","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>.","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>","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>","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.","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>.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal of Functional Analysis 279 (2020)."},"year":"2020","volume":279,"acknowledgement":"Partially supported by ERC Advanced Grant RANMAT No. 338804."},{"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/2002.00859"}],"oa":1,"publication_identifier":{"eissn":["10886850"],"issn":["00029947"]},"type":"journal_article","date_published":"2020-08-01T00:00:00Z","keyword":["Wasserstein space","isometric embeddings","isometric rigidity","exotic isometry flow"],"language":[{"iso":"eng"}],"month":"08","project":[{"name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294","call_identifier":"H2020","_id":"26A455A6-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","publication":"Transactions of the American Mathematical Society","ddc":["515"],"volume":373,"abstract":[{"lang":"eng","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))."}],"day":"01","doi":"10.1090/tran/8113","arxiv":1,"external_id":{"isi":["000551418100018"],"arxiv":["2002.00859"]},"isi":1,"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>.","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.","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>","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.","short":"G.P. Geher, T. Titkos, D. Virosztek, Transactions of the American Mathematical Society 373 (2020) 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>."},"year":"2020","date_updated":"2023-08-17T14:31:03Z","article_type":"original","publisher":"American Mathematical Society","quality_controlled":"1","ec_funded":1,"page":"5855-5883","intvolume":"       373","title":"Isometric study of Wasserstein spaces - the real line","date_created":"2020-01-29T10:20:46Z","department":[{"_id":"LaEr"}],"article_processing_charge":"No","publication_status":"published","issue":"8","author":[{"last_name":"Geher","first_name":"Gyorgy Pal","full_name":"Geher, Gyorgy Pal"},{"full_name":"Titkos, Tamas","last_name":"Titkos","first_name":"Tamas"},{"first_name":"Daniel","last_name":"Virosztek","orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"_id":"7389"},{"type":"journal_article","date_published":"2020-07-01T00:00:00Z","publication_identifier":{"eissn":["10960783"],"issn":["00221236"]},"oa":1,"main_file_link":[{"url":"https://arxiv.org/abs/1804.11340","open_access":"1"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication":"Journal of Functional Analysis","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"}],"oa_version":"Preprint","article_number":"108507","month":"07","language":[{"iso":"eng"}],"year":"2020","citation":{"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>","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>","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>.","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.","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>.","ista":"Erdös L, Krüger TH, Nemish Y. 2020. Local laws for polynomials of Wigner matrices. Journal of Functional Analysis. 278(12), 108507."},"date_updated":"2023-08-18T06:36:10Z","external_id":{"arxiv":["1804.11340"],"isi":["000522798900001"]},"isi":1,"day":"01","doi":"10.1016/j.jfa.2020.108507","arxiv":1,"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"}],"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","volume":278,"scopus_import":"1","_id":"7512","issue":"12","author":[{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","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"},{"orcid":"0000-0002-7327-856X","full_name":"Nemish, Yuriy","first_name":"Yuriy","last_name":"Nemish","id":"4D902E6A-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","date_created":"2020-02-23T23:00:36Z","department":[{"_id":"LaEr"}],"publication_status":"published","intvolume":"       278","title":"Local laws for polynomials of Wigner matrices","ec_funded":1,"quality_controlled":"1","publisher":"Elsevier","article_type":"original"},{"date_published":"2020-08-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["0377-9017"],"eissn":["1573-0530"]},"oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1903.10455"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","status":"public","publication":"Letters in Mathematical Physics","oa_version":"Preprint","project":[{"_id":"26A455A6-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"Geometric study of Wasserstein spaces and free probability","grant_number":"846294"},{"grant_number":"291734","name":"International IST Postdoc Fellowship Programme","_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"}],"month":"08","language":[{"iso":"eng"}],"date_updated":"2023-08-18T10:17:26Z","citation":{"ista":"Pitrik J, Virosztek D. 2020. Quantum Hellinger distances revisited. Letters in Mathematical Physics. 110(8), 2039–2052.","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>.","short":"J. Pitrik, D. Virosztek, Letters in Mathematical Physics 110 (2020) 2039–2052.","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>.","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.","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>","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>"},"year":"2020","isi":1,"external_id":{"isi":["000551556000002"],"arxiv":["1903.10455"]},"arxiv":1,"doi":"10.1007/s11005-020-01282-0","day":"01","abstract":[{"lang":"eng","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. "}],"volume":110,"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.","_id":"7618","scopus_import":"1","author":[{"full_name":"Pitrik, Jozsef","last_name":"Pitrik","first_name":"Jozsef"},{"last_name":"Virosztek","first_name":"Daniel","full_name":"Virosztek, Daniel","orcid":"0000-0003-1109-5511","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"issue":"8","publication_status":"published","department":[{"_id":"LaEr"}],"article_processing_charge":"No","date_created":"2020-03-25T15:57:48Z","title":"Quantum Hellinger distances revisited","intvolume":"       110","page":"2039-2052","ec_funded":1,"quality_controlled":"1","publisher":"Springer Nature","article_type":"original"},{"volume":48,"isi":1,"external_id":{"isi":["000528269100013"],"arxiv":["1804.07744"]},"date_updated":"2024-02-22T14:34:33Z","year":"2020","citation":{"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>.","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.","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>","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>","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>.","short":"J. Alt, L. Erdös, T.H. Krüger, D.J. Schröder, Annals of Probability 48 (2020) 963–1001."},"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"}],"doi":"10.1214/19-AOP1379","arxiv":1,"day":"01","page":"963-1001","ec_funded":1,"quality_controlled":"1","article_type":"original","publisher":"Institute of Mathematical Statistics","author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","last_name":"Alt","first_name":"Johannes","full_name":"Alt, Johannes"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","id":"3020C786-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","last_name":"Schröder","first_name":"Dominik J","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856"}],"issue":"2","_id":"6184","scopus_import":"1","title":"Correlated random matrices: Band rigidity and edge universality","intvolume":"        48","publication_status":"published","article_processing_charge":"No","department":[{"_id":"LaEr"}],"date_created":"2019-03-28T09:20:08Z","status":"public","user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","related_material":{"record":[{"status":"public","relation":"dissertation_contains","id":"149"},{"status":"public","relation":"dissertation_contains","id":"6179"}]},"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.07744"}],"date_published":"2020-03-01T00:00:00Z","type":"journal_article","oa":1,"publication_identifier":{"issn":["0091-1798"]},"language":[{"iso":"eng"}],"publication":"Annals of Probability","month":"03","oa_version":"Preprint","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}]},{"ddc":["530","510"],"volume":378,"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.","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"}],"doi":"10.1007/s00220-019-03657-4","arxiv":1,"day":"01","isi":1,"external_id":{"arxiv":["1809.03971"],"isi":["000529483000001"]},"date_updated":"2023-09-07T12:54:12Z","citation":{"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.","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>.","short":"L. Erdös, T.H. Krüger, D.J. Schröder, Communications in Mathematical Physics 378 (2020) 1203–1278.","ieee":"L. Erdös, T. H. Krüger, and D. J. Schröder, “Cusp universality for random matrices I: Local law and the complex Hermitian case,” <i>Communications in Mathematical Physics</i>, vol. 378. Springer Nature, pp. 1203–1278, 2020.","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>"},"year":"2020","article_type":"original","publisher":"Springer Nature","file_date_updated":"2020-11-18T11:14:37Z","page":"1203-1278","quality_controlled":"1","ec_funded":1,"title":"Cusp universality for random matrices I: Local law and the complex Hermitian case","intvolume":"       378","publication_status":"published","date_created":"2019-03-28T10:21:15Z","department":[{"_id":"LaEr"}],"article_processing_charge":"Yes (via OA deal)","author":[{"last_name":"Erdös","first_name":"László","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","first_name":"Torben H"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J"}],"_id":"6185","scopus_import":"1","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","related_material":{"record":[{"relation":"dissertation_contains","id":"6179","status":"public"}]},"file":[{"file_id":"8771","creator":"dernst","relation":"main_file","access_level":"open_access","success":1,"date_updated":"2020-11-18T11:14:37Z","file_name":"2020_CommMathPhysics_Erdoes.pdf","content_type":"application/pdf","date_created":"2020-11-18T11:14:37Z","checksum":"c3a683e2afdcea27afa6880b01e53dc2","file_size":2904574}],"oa":1,"publication_identifier":{"eissn":["1432-0916"],"issn":["0010-3616"]},"date_published":"2020-09-01T00:00:00Z","type":"journal_article","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"language":[{"iso":"eng"}],"month":"09","oa_version":"Published Version","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"publication":"Communications in Mathematical Physics","has_accepted_license":"1"},{"publisher":"World Scientific Publishing","article_type":"original","ec_funded":1,"quality_controlled":"1","date_created":"2019-05-26T21:59:14Z","department":[{"_id":"LaEr"}],"article_processing_charge":"No","publication_status":"published","intvolume":"         9","title":"Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices","scopus_import":"1","_id":"6488","issue":"3","author":[{"first_name":"Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"}],"volume":9,"day":"01","doi":"10.1142/S2010326320500069","arxiv":1,"abstract":[{"lang":"eng","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."}],"citation":{"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.","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>","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>","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.","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>.","short":"G. Cipolloni, L. Erdös, Random Matrices: Theory and Application 9 (2020)."},"year":"2020","date_updated":"2023-08-28T08:38:48Z","external_id":{"isi":["000547464400001"],"arxiv":["1806.08751"]},"isi":1,"language":[{"iso":"eng"}],"project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"grant_number":"665385","name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"oa_version":"Preprint","article_number":"2050006","month":"07","publication":"Random Matrices: Theory and Application","main_file_link":[{"url":"https://arxiv.org/abs/1806.08751","open_access":"1"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","publication_identifier":{"issn":["20103263"],"eissn":["20103271"]},"oa":1,"type":"journal_article","date_published":"2020-07-01T00:00:00Z"},{"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."}],"day":"01","arxiv":1,"doi":"10.4171/dm/780","external_id":{"arxiv":["1804.07752"]},"citation":{"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.","short":"J. Alt, L. Erdös, T.H. Krüger, Documenta Mathematica 25 (2020) 1421–1539.","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>.","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.","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>.","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>"},"year":"2020","date_updated":"2023-12-18T10:46:09Z","ddc":["510"],"volume":25,"intvolume":"        25","title":"The Dyson equation with linear self-energy: Spectral bands, edges and cusps","department":[{"_id":"LaEr"}],"date_created":"2023-12-18T10:37:43Z","article_processing_charge":"Yes","publication_status":"published","author":[{"id":"36D3D8B6-F248-11E8-B48F-1D18A9856A87","full_name":"Alt, Johannes","first_name":"Johannes","last_name":"Alt"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H","last_name":"Krüger","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H"}],"_id":"14694","article_type":"original","publisher":"EMS Press","file_date_updated":"2023-12-18T10:42:32Z","quality_controlled":"1","page":"1421-1539","oa":1,"publication_identifier":{"eissn":["1431-0643"],"issn":["1431-0635"]},"type":"journal_article","date_published":"2020-09-01T00:00:00Z","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)"},"related_material":{"record":[{"status":"public","id":"6183","relation":"earlier_version"}]},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","file":[{"file_id":"14695","creator":"dernst","success":1,"access_level":"open_access","relation":"main_file","date_updated":"2023-12-18T10:42:32Z","content_type":"application/pdf","file_name":"2020_DocumentaMathematica_Alt.pdf","date_created":"2023-12-18T10:42:32Z","checksum":"12aacc1d63b852ff9a51c1f6b218d4a6","file_size":1374708}],"month":"09","oa_version":"Published Version","has_accepted_license":"1","publication":"Documenta Mathematica","keyword":["General Mathematics"],"language":[{"iso":"eng"}]},{"article_processing_charge":"No","department":[{"_id":"LaEr"}],"date_created":"2024-03-04T10:27:57Z","publication_status":"published","intvolume":"         1","title":"Optimal lower bound on the least singular value of the shifted Ginibre ensemble","scopus_import":"1","_id":"15063","issue":"1","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","last_name":"Cipolloni","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","first_name":"Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J"}],"publisher":"Mathematical Sciences Publishers","article_type":"original","quality_controlled":"1","ec_funded":1,"page":"101-146","day":"16","doi":"10.2140/pmp.2020.1.101","arxiv":1,"abstract":[{"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).","lang":"eng"}],"citation":{"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>.","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.","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>","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>","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.","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>."},"year":"2020","date_updated":"2024-03-04T10:33:15Z","external_id":{"arxiv":["1908.01653"]},"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","volume":1,"project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"grant_number":"665385","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"oa_version":"Preprint","month":"11","publication":"Probability and Mathematical Physics","keyword":["General Medicine"],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["2690-1005","2690-0998"]},"oa":1,"type":"journal_article","date_published":"2020-11-16T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1908.01653","open_access":"1"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},{"abstract":[{"lang":"eng","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]."}],"doi":"10.1007/s11854-020-0135-2","arxiv":1,"day":"01","isi":1,"external_id":{"arxiv":["1804.11199"],"isi":["000611879400008"]},"date_updated":"2023-08-24T11:16:03Z","citation":{"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>.","short":"Z. Bao, L. Erdös, K. Schnelli, Journal d’Analyse Mathematique 142 (2020) 323–348.","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>","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>","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>.","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."},"year":"2020","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.","volume":142,"title":"On the support of the free additive convolution","intvolume":"       142","publication_status":"published","department":[{"_id":"LaEr"}],"date_created":"2021-02-07T23:01:15Z","article_processing_charge":"No","author":[{"full_name":"Bao, Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"434AD0AE-F248-11E8-B48F-1D18A9856A87","last_name":"Schnelli","first_name":"Kevin","full_name":"Schnelli, Kevin","orcid":"0000-0003-0954-3231"}],"_id":"9104","scopus_import":"1","article_type":"original","publisher":"Springer Nature","page":"323-348","quality_controlled":"1","ec_funded":1,"oa":1,"publication_identifier":{"eissn":["15658538"],"issn":["00217670"]},"date_published":"2020-11-01T00:00:00Z","type":"journal_article","status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1804.11199"}],"month":"11","oa_version":"Preprint","project":[{"name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"publication":"Journal d'Analyse Mathematique","language":[{"iso":"eng"}]},{"volume":9,"acknowledgement":"M.G. was supported by the DFG under grant GE 2871/1-1.","date_updated":"2023-09-08T11:35:31Z","year":"2019","citation":{"chicago":"Dietlein, Adrian M, Martin Gebert, and Peter Müller. “Perturbations of Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.” <i>Journal of Spectral Theory</i>. European Mathematical Society Publishing House, 2019. <a href=\"https://doi.org/10.4171/jst/267\">https://doi.org/10.4171/jst/267</a>.","ieee":"A. M. Dietlein, M. Gebert, and P. Müller, “Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function,” <i>Journal of Spectral Theory</i>, vol. 9, no. 3. European Mathematical Society Publishing House, pp. 921–965, 2019.","ama":"Dietlein AM, Gebert M, Müller P. Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. <i>Journal of Spectral Theory</i>. 2019;9(3):921-965. doi:<a href=\"https://doi.org/10.4171/jst/267\">10.4171/jst/267</a>","apa":"Dietlein, A. M., Gebert, M., &#38; Müller, P. (2019). Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. <i>Journal of Spectral Theory</i>. European Mathematical Society Publishing House. <a href=\"https://doi.org/10.4171/jst/267\">https://doi.org/10.4171/jst/267</a>","ista":"Dietlein AM, Gebert M, Müller P. 2019. Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function. Journal of Spectral Theory. 9(3), 921–965.","short":"A.M. Dietlein, M. Gebert, P. Müller, Journal of Spectral Theory 9 (2019) 921–965.","mla":"Dietlein, Adrian M., et al. “Perturbations of Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.” <i>Journal of Spectral Theory</i>, vol. 9, no. 3, European Mathematical Society Publishing House, 2019, pp. 921–65, doi:<a href=\"https://doi.org/10.4171/jst/267\">10.4171/jst/267</a>."},"isi":1,"external_id":{"isi":["000484709400006"],"arxiv":["1701.02956"]},"arxiv":1,"doi":"10.4171/jst/267","day":"01","abstract":[{"lang":"eng","text":"We study effects of a bounded and compactly supported perturbation on multidimensional continuum random Schrödinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schrödinger operators. Among others, we prove that Anderson orthogonality does occur for Fermi energies in the region of complete localisation with a non-zero probability. This partially confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11 (2015), 560–565]. The spectral shift function plays an important role in our analysis of Anderson orthogonality. We identify it with the index of the corresponding pair of spectral projections and explore the consequences thereof. All our results rely on the main technical estimate of this paper which guarantees separate exponential decay of the disorder-averaged Schatten p-norm of χa(f(H)−f(Hτ))χb in a and b. Here, Hτ is a perturbation of the random Schrödinger operator H, χa is the multiplication operator corresponding to the indicator function of a unit cube centred about a∈Rd, and f is in a suitable class of functions of bounded variation with distributional derivative supported in the region of complete localisation for H."}],"page":"921-965","quality_controlled":"1","publisher":"European Mathematical Society Publishing House","article_type":"original","_id":"10879","scopus_import":"1","author":[{"full_name":"Dietlein, Adrian M","first_name":"Adrian M","last_name":"Dietlein","id":"317CB464-F248-11E8-B48F-1D18A9856A87"},{"last_name":"Gebert","first_name":"Martin","full_name":"Gebert, Martin"},{"full_name":"Müller, Peter","first_name":"Peter","last_name":"Müller"}],"issue":"3","publication_status":"published","department":[{"_id":"LaEr"}],"date_created":"2022-03-18T12:36:42Z","article_processing_charge":"No","title":"Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function","intvolume":"         9","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1701.02956"}],"status":"public","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","date_published":"2019-03-01T00:00:00Z","type":"journal_article","publication_identifier":{"issn":["1664-039X"]},"oa":1,"language":[{"iso":"eng"}],"keyword":["Random Schrödinger operators","spectral shift function","Anderson orthogonality"],"publication":"Journal of Spectral Theory","oa_version":"Preprint","month":"03"},{"date_published":"2019-07-01T00:00:00Z","type":"conference","oa":1,"main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1902.08750"}],"status":"public","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication":"Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics","oa_version":"Preprint","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"_id":"256E75B8-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","grant_number":"716117","name":"Optimal Transport and Stochastic Dynamics"}],"month":"07","article_number":"34","language":[{"iso":"eng"}],"conference":{"name":"FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics","start_date":"2019-07-01","end_date":"2019-07-05","location":"Ljubljana, Slovenia"},"date_updated":"2021-01-12T08:17:18Z","year":"2019","citation":{"ista":"Betea D, Bouttier J, Nejjar P, Vuletíc M. 2019. New edge asymptotics of skew Young diagrams via free boundaries. Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics. FPSAC: International Conference on Formal Power Series and Algebraic Combinatorics, 34.","mla":"Betea, Dan, et al. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>, 34, Formal Power Series and Algebraic Combinatorics, 2019.","short":"D. Betea, J. Bouttier, P. Nejjar, M. Vuletíc, in:, Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics, Formal Power Series and Algebraic Combinatorics, 2019.","ieee":"D. Betea, J. Bouttier, P. Nejjar, and M. Vuletíc, “New edge asymptotics of skew Young diagrams via free boundaries,” in <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>, Ljubljana, Slovenia, 2019.","chicago":"Betea, Dan, Jérémie Bouttier, Peter Nejjar, and Mirjana Vuletíc. “New Edge Asymptotics of Skew Young Diagrams via Free Boundaries.” In <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>. Formal Power Series and Algebraic Combinatorics, 2019.","ama":"Betea D, Bouttier J, Nejjar P, Vuletíc M. New edge asymptotics of skew Young diagrams via free boundaries. In: <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>. Formal Power Series and Algebraic Combinatorics; 2019.","apa":"Betea, D., Bouttier, J., Nejjar, P., &#38; Vuletíc, M. (2019). New edge asymptotics of skew Young diagrams via free boundaries. In <i>Proceedings on the 31st International Conference on Formal Power Series and Algebraic Combinatorics</i>. Ljubljana, Slovenia: Formal Power Series and Algebraic Combinatorics."},"external_id":{"arxiv":["1902.08750"]},"arxiv":1,"day":"01","abstract":[{"text":"We study edge asymptotics of poissonized Plancherel-type measures on skew Young diagrams (integer partitions). These measures can be seen as generalizations of those studied by Baik--Deift--Johansson and Baik--Rains in resolving Ulam's problem on longest increasing subsequences of random permutations and the last passage percolation (corner growth) discrete versions thereof. Moreover they interpolate between said measures and the uniform measure on partitions. In the new KPZ-like 1/3 exponent edge scaling limit with logarithmic corrections, we find new probability distributions generalizing the classical Tracy--Widom GUE, GOE and GSE distributions from the theory of random matrices.","lang":"eng"}],"acknowledgement":"D.B. is especially grateful to Patrik Ferrari for suggesting simplifications in Section 3 and\r\nto Alessandra Occelli for suggesting the name for the models of Section 2.\r\n","_id":"8175","scopus_import":"1","author":[{"first_name":"Dan","last_name":"Betea","full_name":"Betea, Dan"},{"full_name":"Bouttier, Jérémie","last_name":"Bouttier","first_name":"Jérémie"},{"id":"4BF426E2-F248-11E8-B48F-1D18A9856A87","full_name":"Nejjar, Peter","first_name":"Peter","last_name":"Nejjar"},{"full_name":"Vuletíc, Mirjana","first_name":"Mirjana","last_name":"Vuletíc"}],"publication_status":"published","date_created":"2020-07-26T22:01:04Z","article_processing_charge":"No","department":[{"_id":"LaEr"}],"title":"New edge asymptotics of skew Young diagrams via free boundaries","ec_funded":1,"quality_controlled":"1","publisher":"Formal Power Series and Algebraic Combinatorics"},{"volume":480,"citation":{"apa":"Gehér, G. P., Titkos, T., &#38; Virosztek, D. (2019). On isometric embeddings of Wasserstein spaces – the discrete case. <i>Journal of Mathematical Analysis and Applications</i>. Elsevier. <a href=\"https://doi.org/10.1016/j.jmaa.2019.123435\">https://doi.org/10.1016/j.jmaa.2019.123435</a>","ama":"Gehér GP, Titkos T, Virosztek D. On isometric embeddings of Wasserstein spaces – the discrete case. <i>Journal of Mathematical Analysis and Applications</i>. 2019;480(2). doi:<a href=\"https://doi.org/10.1016/j.jmaa.2019.123435\">10.1016/j.jmaa.2019.123435</a>","ieee":"G. P. Gehér, T. Titkos, and D. Virosztek, “On isometric embeddings of Wasserstein spaces – the discrete case,” <i>Journal of Mathematical Analysis and Applications</i>, vol. 480, no. 2. Elsevier, 2019.","chicago":"Gehér, György Pál, Tamás Titkos, and Daniel Virosztek. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” <i>Journal of Mathematical Analysis and Applications</i>. Elsevier, 2019. <a href=\"https://doi.org/10.1016/j.jmaa.2019.123435\">https://doi.org/10.1016/j.jmaa.2019.123435</a>.","short":"G.P. Gehér, T. Titkos, D. Virosztek, Journal of Mathematical Analysis and Applications 480 (2019).","mla":"Gehér, György Pál, et al. “On Isometric Embeddings of Wasserstein Spaces – the Discrete Case.” <i>Journal of Mathematical Analysis and Applications</i>, vol. 480, no. 2, 123435, Elsevier, 2019, doi:<a href=\"https://doi.org/10.1016/j.jmaa.2019.123435\">10.1016/j.jmaa.2019.123435</a>.","ista":"Gehér GP, Titkos T, Virosztek D. 2019. On isometric embeddings of Wasserstein spaces – the discrete case. Journal of Mathematical Analysis and Applications. 480(2), 123435."},"year":"2019","date_updated":"2023-08-29T07:18:50Z","external_id":{"isi":["000486563900031"],"arxiv":["1809.01101"]},"isi":1,"day":"15","arxiv":1,"doi":"10.1016/j.jmaa.2019.123435","abstract":[{"text":"The aim of this short paper is to offer a complete characterization of all (not necessarily surjective) isometric embeddings of the Wasserstein space Wp(X), where S is a countable discrete metric space and 0<p<∞ is any parameter value. Roughly speaking, we will prove that any isometric embedding can be described by a special kind of X×(0,1]-indexed family of nonnegative finite measures. Our result implies that a typical non-surjective isometric embedding of Wp(X) splits mass and does not preserve the shape of measures. In order to stress that the lack of surjectivity is what makes things challenging, we will prove alternatively that Wp(X) is isometrically rigid for all 0<p<∞.","lang":"eng"}],"ec_funded":1,"quality_controlled":"1","publisher":"Elsevier","article_type":"original","scopus_import":"1","_id":"6843","issue":"2","author":[{"last_name":"Gehér","first_name":"György Pál","full_name":"Gehér, György Pál"},{"full_name":"Titkos, Tamás","first_name":"Tamás","last_name":"Titkos"},{"orcid":"0000-0003-1109-5511","full_name":"Virosztek, Daniel","first_name":"Daniel","last_name":"Virosztek","id":"48DB45DA-F248-11E8-B48F-1D18A9856A87"}],"article_processing_charge":"No","department":[{"_id":"LaEr"}],"date_created":"2019-09-01T22:01:01Z","publication_status":"published","intvolume":"       480","title":"On isometric embeddings of Wasserstein spaces – the discrete case","main_file_link":[{"url":"https://arxiv.org/abs/1809.01101","open_access":"1"}],"status":"public","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","type":"journal_article","date_published":"2019-12-15T00:00:00Z","publication_identifier":{"issn":["0022247X"],"eissn":["10960813"]},"oa":1,"language":[{"iso":"eng"}],"publication":"Journal of Mathematical Analysis and Applications","project":[{"_id":"25681D80-B435-11E9-9278-68D0E5697425","call_identifier":"FP7","name":"International IST Postdoc Fellowship Programme","grant_number":"291734"}],"oa_version":"Preprint","article_number":"123435","month":"12"}]