[{"author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","last_name":"Cipolloni"},{"full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","last_name":"Erdös","first_name":"László"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","first_name":"Dominik J","last_name":"Schröder"}],"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","oa":1,"arxiv":1,"department":[{"_id":"LaEr"}],"publication":"Probability Theory and Related Fields","date_updated":"2024-03-07T15:07:53Z","ec_funded":1,"doi":"10.1007/s00440-020-01003-7","scopus_import":"1","article_type":"original","publication_identifier":{"eissn":["14322064"],"issn":["01788051"]},"title":"Edge universality for non-Hermitian random matrices","publication_status":"published","file_date_updated":"2020-10-05T14:53:40Z","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","year":"2021","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. 2021. doi:<a href=\"https://doi.org/10.1007/s00440-020-01003-7\">10.1007/s00440-020-01003-7</a>","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2021.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2021. <a href=\"https://doi.org/10.1007/s00440-020-01003-7\">https://doi.org/10.1007/s00440-020-01003-7</a>.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021).","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2021). Edge universality for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-020-01003-7\">https://doi.org/10.1007/s00440-020-01003-7</a>","mla":"Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2021, doi:<a href=\"https://doi.org/10.1007/s00440-020-01003-7\">10.1007/s00440-020-01003-7</a>."},"abstract":[{"lang":"eng","text":"We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy–Widom distribution at the spectral edges of the Wigner ensemble."}],"_id":"8601","date_created":"2020-10-04T22:01:37Z","file":[{"checksum":"611ae28d6055e1e298d53a57beb05ef4","content_type":"application/pdf","creator":"dernst","file_id":"8612","date_created":"2020-10-05T14:53:40Z","relation":"main_file","date_updated":"2020-10-05T14:53:40Z","file_size":497032,"success":1,"access_level":"open_access","file_name":"2020_ProbTheory_Cipolloni.pdf"}],"publisher":"Springer Nature","external_id":{"isi":["000572724600002"],"arxiv":["1908.00969"]},"date_published":"2021-02-01T00:00:00Z","type":"journal_article","language":[{"iso":"eng"}],"ddc":["510"],"month":"02","isi":1,"status":"public","day":"01","quality_controlled":"1","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804","call_identifier":"FP7"},{"grant_number":"665385","call_identifier":"H2020","name":"International IST Doctoral Program","_id":"2564DBCA-B435-11E9-9278-68D0E5697425"}],"has_accepted_license":"1"},{"intvolume":"       173","department":[{"_id":"JaMa"}],"publication":"Probability Theory and Related Fields","date_updated":"2023-08-24T14:38:32Z","author":[{"first_name":"Mate","last_name":"Gerencser","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87","full_name":"Gerencser, Mate"},{"first_name":"Martin","last_name":"Hairer","full_name":"Hairer, Martin"}],"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","oa":1,"volume":173,"year":"2019","citation":{"ieee":"M. Gerencser and M. Hairer, “Singular SPDEs in domains with boundaries,” <i>Probability Theory and Related Fields</i>, vol. 173, no. 3–4. Springer, pp. 697–758, 2019.","ista":"Gerencser M, Hairer M. 2019. Singular SPDEs in domains with boundaries. Probability Theory and Related Fields. 173(3–4), 697–758.","ama":"Gerencser M, Hairer M. Singular SPDEs in domains with boundaries. <i>Probability Theory and Related Fields</i>. 2019;173(3-4):697–758. doi:<a href=\"https://doi.org/10.1007/s00440-018-0841-1\">10.1007/s00440-018-0841-1</a>","mla":"Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.” <i>Probability Theory and Related Fields</i>, vol. 173, no. 3–4, Springer, 2019, pp. 697–758, doi:<a href=\"https://doi.org/10.1007/s00440-018-0841-1\">10.1007/s00440-018-0841-1</a>.","short":"M. Gerencser, M. Hairer, Probability Theory and Related Fields 173 (2019) 697–758.","apa":"Gerencser, M., &#38; Hairer, M. (2019). Singular SPDEs in domains with boundaries. <i>Probability Theory and Related Fields</i>. Springer. <a href=\"https://doi.org/10.1007/s00440-018-0841-1\">https://doi.org/10.1007/s00440-018-0841-1</a>","chicago":"Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.” <i>Probability Theory and Related Fields</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00440-018-0841-1\">https://doi.org/10.1007/s00440-018-0841-1</a>."},"abstract":[{"lang":"eng","text":"We study spaces of modelled distributions with singular behaviour near the boundary of a domain that, in the context of the theory of regularity structures, allow one to give robust solution theories for singular stochastic PDEs with boundary conditions. The calculus of modelled distributions established in Hairer (Invent Math 198(2):269–504, 2014. https://doi.org/10.1007/s00222-014-0505-4) is extended to this setting. We formulate and solve fixed point problems in these spaces with a class of kernels that is sufficiently large to cover in particular the Dirichlet and Neumann heat kernels. These results are then used to provide solution theories for the KPZ equation with Dirichlet and Neumann boundary conditions and for the 2D generalised parabolic Anderson model with Dirichlet boundary conditions. In the case of the KPZ equation with Neumann boundary conditions, we show that, depending on the class of mollifiers one considers, a “boundary renormalisation” takes place. In other words, there are situations in which a certain boundary condition is applied to an approximation to the KPZ equation, but the limiting process is the Hopf–Cole solution to the KPZ equation with a different boundary condition."}],"_id":"319","file":[{"content_type":"application/pdf","file_id":"5722","creator":"dernst","checksum":"288d16ef7291242f485a9660979486e3","file_name":"2018_ProbTheory_Gerencser.pdf","access_level":"open_access","relation":"main_file","date_updated":"2020-07-14T12:46:03Z","file_size":893182,"date_created":"2018-12-17T16:25:24Z"}],"date_created":"2018-12-11T11:45:48Z","doi":"10.1007/s00440-018-0841-1","scopus_import":"1","article_type":"original","acknowledgement":"MG thanks the support of the LMS Postdoctoral Mobility Grant.\r\n\r\n","publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"publication_status":"published","title":"Singular SPDEs in domains with boundaries","file_date_updated":"2020-07-14T12:46:03Z","oa_version":"Published Version","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"ddc":["510"],"month":"04","isi":1,"status":"public","publist_id":"7546","publisher":"Springer","external_id":{"isi":["000463613800001"]},"date_published":"2019-04-01T00:00:00Z","type":"journal_article","issue":"3-4","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"has_accepted_license":"1","page":"697–758","day":"01","quality_controlled":"1"},{"quality_controlled":"1","day":"01","page":"293–373","project":[{"call_identifier":"FP7","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","short":"CC BY (4.0)"},"has_accepted_license":"1","issue":"1-2","external_id":{"isi":["000459396500007"]},"date_published":"2019-02-01T00:00:00Z","type":"journal_article","publisher":"Springer","status":"public","publist_id":"7394","month":"02","isi":1,"language":[{"iso":"eng"}],"ddc":["510"],"file_date_updated":"2020-07-14T12:46:26Z","article_processing_charge":"Yes (via OA deal)","oa_version":"Published Version","publication_status":"published","title":"Stability of the matrix Dyson equation and random matrices with correlations","article_type":"original","publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\n","doi":"10.1007/s00440-018-0835-z","scopus_import":"1","_id":"429","file":[{"checksum":"f9354fa5c71f9edd17132588f0dc7d01","content_type":"application/pdf","creator":"dernst","file_id":"5720","date_created":"2018-12-17T16:12:08Z","date_updated":"2020-07-14T12:46:26Z","file_size":1201840,"relation":"main_file","file_name":"2018_ProbTheory_Ajanki.pdf","access_level":"open_access"}],"date_created":"2018-12-11T11:46:25Z","abstract":[{"lang":"eng","text":"We consider real symmetric or complex hermitian random matrices with correlated entries. We prove local laws for the resolvent and universality of the local eigenvalue statistics in the bulk of the spectrum. The correlations have fast decay but are otherwise of general form. The key novelty is the detailed stability analysis of the corresponding matrix valued Dyson equation whose solution is the deterministic limit of the resolvent."}],"year":"2019","citation":{"short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.","chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” <i>Probability Theory and Related Fields</i>. Springer, 2019. <a href=\"https://doi.org/10.1007/s00440-018-0835-z\">https://doi.org/10.1007/s00440-018-0835-z</a>.","apa":"Ajanki, O. H., Erdös, L., &#38; Krüger, T. H. (2019). Stability of the matrix Dyson equation and random matrices with correlations. <i>Probability Theory and Related Fields</i>. Springer. <a href=\"https://doi.org/10.1007/s00440-018-0835-z\">https://doi.org/10.1007/s00440-018-0835-z</a>","mla":"Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” <i>Probability Theory and Related Fields</i>, vol. 173, no. 1–2, Springer, 2019, pp. 293–373, doi:<a href=\"https://doi.org/10.1007/s00440-018-0835-z\">10.1007/s00440-018-0835-z</a>.","ama":"Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random matrices with correlations. <i>Probability Theory and Related Fields</i>. 2019;173(1-2):293–373. doi:<a href=\"https://doi.org/10.1007/s00440-018-0835-z\">10.1007/s00440-018-0835-z</a>","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation and random matrices with correlations,” <i>Probability Theory and Related Fields</i>, vol. 173, no. 1–2. Springer, pp. 293–373, 2019.","ista":"Ajanki OH, Erdös L, Krüger TH. 2019. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 173(1–2), 293–373."},"oa":1,"volume":173,"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","author":[{"last_name":"Ajanki","first_name":"Oskari H","full_name":"Ajanki, Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Erdös, László","orcid":"0000-0001-5366-9603","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","first_name":"László"},{"last_name":"Krüger","first_name":"Torben H","full_name":"Krüger, Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297"}],"publication":"Probability Theory and Related Fields","ec_funded":1,"date_updated":"2023-08-24T14:39:00Z","department":[{"_id":"LaEr"}],"intvolume":"       173"}]