[{"project":[{"grant_number":"754411","_id":"260C2330-B435-11E9-9278-68D0E5697425","call_identifier":"H2020","name":"ISTplus - Postdoctoral Fellowships"},{"name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","_id":"62796744-2b32-11ec-9570-940b20777f1d","grant_number":"101020331"}],"language":[{"iso":"eng"}],"isi":1,"publication_identifier":{"eissn":["1083-589X"]},"quality_controlled":"1","doi":"10.1214/23-ECP516","department":[{"_id":"LaEr"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Institute of Mathematical Statistics","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"article_type":"original","scopus_import":"1","article_processing_charge":"No","ec_funded":1,"publication":"Electronic Communications in Probability","file":[{"creator":"dernst","file_size":479105,"content_type":"application/pdf","relation":"main_file","file_name":"2023_ElectCommProbability_Dubach.pdf","success":1,"access_level":"open_access","date_created":"2023-02-27T09:43:27Z","checksum":"a1c6f0a3e33688fd71309c86a9aad86e","file_id":"12692","date_updated":"2023-02-27T09:43:27Z"}],"day":"08","author":[{"id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume","last_name":"Dubach","first_name":"Guillaume"},{"first_name":"László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"}],"title":"Dynamics of a rank-one perturbation of a Hermitian matrix","arxiv":1,"status":"public","external_id":{"isi":["000950650200005"],"arxiv":["2108.13694"]},"citation":{"ama":"Dubach G, Erdös L. Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. 2023;28:1-13. doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>","ista":"Dubach G, Erdös L. 2023. Dynamics of a rank-one perturbation of a Hermitian matrix. Electronic Communications in Probability. 28, 1–13.","mla":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>, vol. 28, Institute of Mathematical Statistics, 2023, pp. 1–13, doi:<a href=\"https://doi.org/10.1214/23-ECP516\">10.1214/23-ECP516</a>.","apa":"Dubach, G., &#38; Erdös, L. (2023). Dynamics of a rank-one perturbation of a Hermitian matrix. <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>","ieee":"G. Dubach and L. Erdös, “Dynamics of a rank-one perturbation of a Hermitian matrix,” <i>Electronic Communications in Probability</i>, vol. 28. Institute of Mathematical Statistics, pp. 1–13, 2023.","chicago":"Dubach, Guillaume, and László Erdös. “Dynamics of a Rank-One Perturbation of a Hermitian Matrix.” <i>Electronic Communications in Probability</i>. Institute of Mathematical Statistics, 2023. <a href=\"https://doi.org/10.1214/23-ECP516\">https://doi.org/10.1214/23-ECP516</a>.","short":"G. Dubach, L. Erdös, Electronic Communications in Probability 28 (2023) 1–13."},"intvolume":"        28","has_accepted_license":"1","oa":1,"publication_status":"published","ddc":["510"],"date_published":"2023-02-08T00:00:00Z","year":"2023","acknowledgement":"G. Dubach gratefully acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. L. Erdős is supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","_id":"12683","type":"journal_article","month":"02","oa_version":"Published Version","abstract":[{"text":"We study the eigenvalue trajectories of a time dependent matrix Gt=H+itvv∗ for t≥0, where H is an N×N Hermitian random matrix and v is a unit vector. In particular, we establish that with high probability, an outlier can be distinguished at all times t>1+N−1/3+ϵ, for any ϵ>0. The study of this natural process combines elements of Hermitian and non-Hermitian analysis, and illustrates some aspects of the intrinsic instability of (even weakly) non-Hermitian matrices.","lang":"eng"}],"date_updated":"2023-10-17T12:48:10Z","page":"1-13","file_date_updated":"2023-02-27T09:43:27Z","date_created":"2023-02-26T23:01:01Z","volume":28},{"_id":"9230","publication":"arXiv","ec_funded":1,"article_processing_charge":"No","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.","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","department":[{"_id":"LaEr"}],"year":"2021","article_number":"2103.04817","arxiv":1,"title":"Maxima of a random model of the Riemann zeta function over intervals of varying length","date_created":"2021-03-09T11:08:15Z","author":[{"first_name":"Louis-Pierre","last_name":"Arguin","full_name":"Arguin, Louis-Pierre"},{"last_name":"Dubach","first_name":"Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume"},{"last_name":"Hartung","first_name":"Lisa","full_name":"Hartung, Lisa"}],"type":"preprint","oa_version":"Preprint","month":"03","date_updated":"2023-05-03T10:22:59Z","day":"08","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."}],"citation":{"ista":"Arguin L-P, Dubach G, Hartung L. Maxima of a random model of the Riemann zeta function over intervals of varying length. arXiv, 2103.04817.","mla":"Arguin, Louis-Pierre, et al. “Maxima of a Random Model of the Riemann Zeta Function over Intervals of Varying Length.” <i>ArXiv</i>, 2103.04817, 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>","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>","short":"L.-P. Arguin, G. Dubach, L. Hartung, ArXiv (n.d.).","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>."},"language":[{"iso":"eng"}],"project":[{"grant_number":"754411","name":"ISTplus - Postdoctoral Fellowships","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425"}],"external_id":{"arxiv":["2103.04817"]},"status":"public","date_published":"2021-03-08T00:00:00Z","doi":"10.48550/arXiv.2103.04817","main_file_link":[{"url":"https://arxiv.org/abs/2103.04817","open_access":"1"}],"oa":1,"publication_status":"submitted"},{"article_number":"2103.11389","title":"Formal verification of Zagier's one-sentence proof","arxiv":1,"date_created":"2021-03-23T05:38:48Z","author":[{"first_name":"Guillaume","last_name":"Dubach","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137","full_name":"Dubach, Guillaume"},{"orcid":"0000-0003-1548-0177","id":"6395C5F6-89DF-11E9-9C97-6BDFE5697425","full_name":"Mühlböck, Fabian","last_name":"Mühlböck","first_name":"Fabian"}],"month":"03","oa_version":"Preprint","type":"preprint","date_updated":"2023-05-03T10:26:45Z","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"}],"_id":"9281","publication":"arXiv","ec_funded":1,"article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2021","department":[{"_id":"LaEr"},{"_id":"ToHe"}],"doi":"10.48550/arXiv.2103.11389","date_published":"2021-03-21T00:00:00Z","main_file_link":[{"url":"https://arxiv.org/abs/2103.11389","open_access":"1"}],"publication_status":"submitted","oa":1,"related_material":{"record":[{"relation":"other","id":"9946","status":"public"}]},"language":[{"iso":"eng"}],"citation":{"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>.","short":"G. Dubach, F. Mühlböck, ArXiv (n.d.).","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>","ista":"Dubach G, Mühlböck F. Formal verification of Zagier’s one-sentence proof. arXiv, 2103.11389.","mla":"Dubach, Guillaume, and Fabian Mühlböck. “Formal Verification of Zagier’s One-Sentence Proof.” <i>ArXiv</i>, 2103.11389, 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>"},"project":[{"grant_number":"754411","call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships"}],"status":"public","external_id":{"arxiv":["2103.11389"]}},{"date_published":"2021-09-28T00:00:00Z","ddc":["519"],"has_accepted_license":"1","oa":1,"publication_status":"published","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>.","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>","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>."},"intvolume":"        26","status":"public","file_date_updated":"2021-11-15T10:10:17Z","date_created":"2021-11-14T23:01:25Z","volume":26,"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"}],"date_updated":"2021-11-15T10:48:46Z","month":"09","type":"journal_article","oa_version":"Published Version","_id":"10285","year":"2021","acknowledgement":"We acknowledge partial support from the grants NSF DMS-1812114 of P. Bourgade (PI) and NSF CAREER DMS-1653602 of L.-P. Arguin (PI). This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement No. 754411. We would like to thank Paul Bourgade and László Erdős for many helpful comments.","quality_controlled":"1","doi":"10.1214/21-EJP686","publication_identifier":{"eissn":["1083-6489"]},"language":[{"iso":"eng"}],"project":[{"call_identifier":"H2020","_id":"260C2330-B435-11E9-9278-68D0E5697425","name":"ISTplus - Postdoctoral Fellowships","grant_number":"754411"}],"title":"On eigenvector statistics in the spherical and truncated unitary ensembles","article_number":"124","file":[{"success":1,"file_name":"2021_ElecJournalProb_Dubach.pdf","creator":"cchlebak","relation":"main_file","content_type":"application/pdf","file_size":735940,"checksum":"1c975afb31460277ce4d22b93538e5f9","date_updated":"2021-11-15T10:10:17Z","file_id":"10288","access_level":"open_access","date_created":"2021-11-15T10:10:17Z"}],"day":"28","author":[{"first_name":"Guillaume","last_name":"Dubach","full_name":"Dubach, Guillaume","id":"D5C6A458-10C4-11EA-ABF4-A4B43DDC885E","orcid":"0000-0001-6892-8137"}],"scopus_import":"1","article_processing_charge":"No","ec_funded":1,"article_type":"original","tmp":{"legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)"},"publication":"Electronic Journal of Probability","department":[{"_id":"LaEr"}],"publisher":"Institute of Mathematical Statistics","user_id":"8b945eb4-e2f2-11eb-945a-df72226e66a9"}]