[{"abstract":[{"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.","lang":"eng"}],"oa_version":"Published Version","scopus_import":"1","month":"02","publication_identifier":{"eissn":["14322064"],"issn":["01788051"]},"publication_status":"published","file":[{"file_name":"2020_ProbTheory_Cipolloni.pdf","date_created":"2020-10-05T14:53:40Z","creator":"dernst","file_size":497032,"date_updated":"2020-10-05T14:53:40Z","success":1,"checksum":"611ae28d6055e1e298d53a57beb05ef4","file_id":"8612","relation":"main_file","access_level":"open_access","content_type":"application/pdf"}],"language":[{"iso":"eng"}],"ec_funded":1,"_id":"8601","type":"journal_article","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)"},"status":"public","date_updated":"2024-03-07T15:07:53Z","ddc":["510"],"department":[{"_id":"LaEr"}],"file_date_updated":"2020-10-05T14:53:40Z","publisher":"Springer Nature","quality_controlled":"1","oa":1,"has_accepted_license":"1","isi":1,"year":"2021","day":"01","publication":"Probability Theory and Related Fields","date_published":"2021-02-01T00:00:00Z","doi":"10.1007/s00440-020-01003-7","date_created":"2020-10-04T22:01:37Z","project":[{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"},{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","name":"Random matrices, universality and disordered quantum systems","grant_number":"338804"},{"name":"International IST Doctoral Program","grant_number":"665385","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","call_identifier":"H2020"}],"citation":{"ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields. Springer Nature, 2021. https://doi.org/10.1007/s00440-020-01003-7.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields (2021).","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Edge universality for non-Hermitian random matrices,” Probability Theory and Related Fields. Springer Nature, 2021.","apa":"Cipolloni, G., Erdös, L., & Schröder, D. J. (2021). Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. Springer Nature. https://doi.org/10.1007/s00440-020-01003-7","ama":"Cipolloni G, Erdös L, Schröder DJ. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields. 2021. doi:10.1007/s00440-020-01003-7","mla":"Cipolloni, Giorgio, et al. “Edge Universality for Non-Hermitian Random Matrices.” Probability Theory and Related Fields, Springer Nature, 2021, doi:10.1007/s00440-020-01003-7."},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","first_name":"Giorgio","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","first_name":"László","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"},{"full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"external_id":{"isi":["000572724600002"],"arxiv":["1908.00969"]},"article_processing_charge":"Yes (via OA deal)","title":"Edge universality for non-Hermitian random matrices"},{"_id":"319","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","type":"journal_article","status":"public","date_updated":"2023-08-24T14:38:32Z","ddc":["510"],"department":[{"_id":"JaMa"}],"file_date_updated":"2020-07-14T12:46:03Z","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."}],"oa_version":"Published Version","scopus_import":"1","intvolume":" 173","month":"04","publication_status":"published","publication_identifier":{"eissn":["14322064"],"issn":["01788051"]},"language":[{"iso":"eng"}],"file":[{"access_level":"open_access","relation":"main_file","content_type":"application/pdf","file_id":"5722","checksum":"288d16ef7291242f485a9660979486e3","creator":"dernst","date_updated":"2020-07-14T12:46:03Z","file_size":893182,"date_created":"2018-12-17T16:25:24Z","file_name":"2018_ProbTheory_Gerencser.pdf"}],"volume":173,"issue":"3-4","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"citation":{"chicago":"Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.” Probability Theory and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0841-1.","ista":"Gerencser M, Hairer M. 2019. Singular SPDEs in domains with boundaries. Probability Theory and Related Fields. 173(3–4), 697–758.","mla":"Gerencser, Mate, and Martin Hairer. “Singular SPDEs in Domains with Boundaries.” Probability Theory and Related Fields, vol. 173, no. 3–4, Springer, 2019, pp. 697–758, doi:10.1007/s00440-018-0841-1.","ieee":"M. Gerencser and M. Hairer, “Singular SPDEs in domains with boundaries,” Probability Theory and Related Fields, vol. 173, no. 3–4. Springer, pp. 697–758, 2019.","short":"M. Gerencser, M. Hairer, Probability Theory and Related Fields 173 (2019) 697–758.","ama":"Gerencser M, Hairer M. Singular SPDEs in domains with boundaries. Probability Theory and Related Fields. 2019;173(3-4):697–758. doi:10.1007/s00440-018-0841-1","apa":"Gerencser, M., & Hairer, M. (2019). Singular SPDEs in domains with boundaries. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-018-0841-1"},"user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000463613800001"]},"author":[{"id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87","first_name":"Mate","last_name":"Gerencser","full_name":"Gerencser, Mate"},{"full_name":"Hairer, Martin","last_name":"Hairer","first_name":"Martin"}],"publist_id":"7546","title":"Singular SPDEs in domains with boundaries","acknowledgement":"MG thanks the support of the LMS Postdoctoral Mobility Grant.\r\n\r\n","oa":1,"quality_controlled":"1","publisher":"Springer","year":"2019","has_accepted_license":"1","isi":1,"publication":"Probability Theory and Related Fields","day":"01","page":"697–758","date_created":"2018-12-11T11:45:48Z","doi":"10.1007/s00440-018-0841-1","date_published":"2019-04-01T00:00:00Z"},{"intvolume":" 173","month":"02","scopus_import":"1","oa_version":"Published Version","abstract":[{"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.","lang":"eng"}],"ec_funded":1,"issue":"1-2","volume":173,"language":[{"iso":"eng"}],"file":[{"file_name":"2018_ProbTheory_Ajanki.pdf","date_created":"2018-12-17T16:12:08Z","file_size":1201840,"date_updated":"2020-07-14T12:46:26Z","creator":"dernst","checksum":"f9354fa5c71f9edd17132588f0dc7d01","file_id":"5720","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"publication_status":"published","publication_identifier":{"issn":["01788051"],"eissn":["14322064"]},"status":"public","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","type":"journal_article","_id":"429","file_date_updated":"2020-07-14T12:46:26Z","department":[{"_id":"LaEr"}],"ddc":["510"],"date_updated":"2023-08-24T14:39:00Z","oa":1,"publisher":"Springer","quality_controlled":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\n","date_created":"2018-12-11T11:46:25Z","doi":"10.1007/s00440-018-0835-z","date_published":"2019-02-01T00:00:00Z","page":"293–373","publication":"Probability Theory and Related Fields","day":"01","year":"2019","isi":1,"has_accepted_license":"1","project":[{"call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804","name":"Random matrices, universality and disordered quantum systems"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"title":"Stability of the matrix Dyson equation and random matrices with correlations","external_id":{"isi":["000459396500007"]},"article_processing_charge":"Yes (via OA deal)","author":[{"first_name":"Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","last_name":"Ajanki","full_name":"Ajanki, Oskari H"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","orcid":"0000-0001-5366-9603","full_name":"Erdös, László"},{"orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H","id":"3020C786-F248-11E8-B48F-1D18A9856A87"}],"publist_id":"7394","user_id":"4359f0d1-fa6c-11eb-b949-802e58b17ae8","citation":{"ama":"Ajanki OH, Erdös L, Krüger TH. Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. 2019;173(1-2):293–373. doi:10.1007/s00440-018-0835-z","apa":"Ajanki, O. H., Erdös, L., & Krüger, T. H. (2019). Stability of the matrix Dyson equation and random matrices with correlations. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-018-0835-z","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Stability of the matrix Dyson equation and random matrices with correlations,” Probability Theory and Related Fields, vol. 173, no. 1–2. Springer, pp. 293–373, 2019.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.","mla":"Ajanki, Oskari H., et al. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields, vol. 173, no. 1–2, Springer, 2019, pp. 293–373, doi:10.1007/s00440-018-0835-z.","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.","chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Stability of the Matrix Dyson Equation and Random Matrices with Correlations.” Probability Theory and Related Fields. Springer, 2019. https://doi.org/10.1007/s00440-018-0835-z."}},{"day":"01","publication":"Probability Theory and Related Fields","isi":1,"has_accepted_license":"1","year":"2017","date_published":"2017-04-01T00:00:00Z","doi":"10.1007/s00440-015-0692-y","date_created":"2018-12-11T11:52:32Z","page":"673 - 776","acknowledgement":"Z. Bao was supported by ERC Advanced Grant RANMAT No. 338804; L. Erdős was partially supported by ERC Advanced Grant RANMAT No. 338804.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria). The authors are very grateful to the anonymous referees for careful reading and valuable comments, which helped to improve the organization.","quality_controlled":"1","publisher":"Springer","oa":1,"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","citation":{"mla":"Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block Band Matrices.” Probability Theory and Related Fields, vol. 167, no. 3–4, Springer, 2017, pp. 673–776, doi:10.1007/s00440-015-0692-y.","apa":"Bao, Z., & Erdös, L. (2017). Delocalization for a class of random block band matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-015-0692-y","ama":"Bao Z, Erdös L. Delocalization for a class of random block band matrices. Probability Theory and Related Fields. 2017;167(3-4):673-776. doi:10.1007/s00440-015-0692-y","short":"Z. Bao, L. Erdös, Probability Theory and Related Fields 167 (2017) 673–776.","ieee":"Z. Bao and L. Erdös, “Delocalization for a class of random block band matrices,” Probability Theory and Related Fields, vol. 167, no. 3–4. Springer, pp. 673–776, 2017.","chicago":"Bao, Zhigang, and László Erdös. “Delocalization for a Class of Random Block Band Matrices.” Probability Theory and Related Fields. Springer, 2017. https://doi.org/10.1007/s00440-015-0692-y.","ista":"Bao Z, Erdös L. 2017. Delocalization for a class of random block band matrices. Probability Theory and Related Fields. 167(3–4), 673–776."},"title":"Delocalization for a class of random block band matrices","author":[{"last_name":"Bao","orcid":"0000-0003-3036-1475","full_name":"Bao, Zhigang","first_name":"Zhigang","id":"442E6A6C-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603"}],"publist_id":"5644","external_id":{"isi":["000398842700004"]},"article_processing_charge":"Yes (via OA deal)","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425"}],"file":[{"content_type":"application/pdf","relation":"main_file","access_level":"open_access","checksum":"67afa85ff1e220cbc1f9f477a828513c","file_id":"4665","file_size":1615755,"date_updated":"2020-07-14T12:45:00Z","creator":"system","file_name":"IST-2016-489-v1+1_s00440-015-0692-y.pdf","date_created":"2018-12-12T10:08:05Z"}],"language":[{"iso":"eng"}],"publication_identifier":{"issn":["01788051"]},"publication_status":"published","volume":167,"issue":"3-4","ec_funded":1,"oa_version":"Published Version","abstract":[{"text":"We consider N×N Hermitian random matrices H consisting of blocks of size M≥N6/7. The matrix elements are i.i.d. within the blocks, close to a Gaussian in the four moment matching sense, but their distribution varies from block to block to form a block-band structure, with an essential band width M. We show that the entries of the Green’s function G(z)=(H−z)−1 satisfy the local semicircle law with spectral parameter z=E+iη down to the real axis for any η≫N−1, using a combination of the supersymmetry method inspired by Shcherbina (J Stat Phys 155(3): 466–499, 2014) and the Green’s function comparison strategy. Previous estimates were valid only for η≫M−1. The new estimate also implies that the eigenvectors in the middle of the spectrum are fully delocalized.","lang":"eng"}],"month":"04","intvolume":" 167","scopus_import":"1","ddc":["530"],"date_updated":"2023-09-20T09:42:12Z","department":[{"_id":"LaEr"}],"file_date_updated":"2020-07-14T12:45:00Z","_id":"1528","status":"public","pubrep_id":"489","article_type":"original","type":"journal_article","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)"}},{"oa":1,"publisher":"Springer","quality_controlled":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). ","page":"667 - 727","date_created":"2018-12-11T11:51:27Z","doi":"10.1007/s00440-016-0740-2","date_published":"2017-12-01T00:00:00Z","year":"2017","has_accepted_license":"1","isi":1,"publication":"Probability Theory and Related Fields","day":"01","project":[{"grant_number":"338804","name":"Random matrices, universality and disordered quantum systems","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","call_identifier":"FP7"},{"name":"IST Austria Open Access Fund","_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854"}],"article_processing_charge":"Yes (via OA deal)","external_id":{"isi":["000414358400002"]},"publist_id":"5930","author":[{"first_name":"Oskari H","id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","full_name":"Ajanki, Oskari H","last_name":"Ajanki"},{"orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"full_name":"Krüger, Torben H","orcid":"0000-0002-4821-3297","last_name":"Krüger","id":"3020C786-F248-11E8-B48F-1D18A9856A87","first_name":"Torben H"}],"title":"Universality for general Wigner-type matrices","citation":{"mla":"Ajanki, Oskari H., et al. “Universality for General Wigner-Type Matrices.” Probability Theory and Related Fields, vol. 169, no. 3–4, Springer, 2017, pp. 667–727, doi:10.1007/s00440-016-0740-2.","apa":"Ajanki, O. H., Erdös, L., & Krüger, T. H. (2017). Universality for general Wigner-type matrices. Probability Theory and Related Fields. Springer. https://doi.org/10.1007/s00440-016-0740-2","ama":"Ajanki OH, Erdös L, Krüger TH. Universality for general Wigner-type matrices. Probability Theory and Related Fields. 2017;169(3-4):667-727. doi:10.1007/s00440-016-0740-2","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 169 (2017) 667–727.","ieee":"O. H. Ajanki, L. Erdös, and T. H. Krüger, “Universality for general Wigner-type matrices,” Probability Theory and Related Fields, vol. 169, no. 3–4. Springer, pp. 667–727, 2017.","chicago":"Ajanki, Oskari H, László Erdös, and Torben H Krüger. “Universality for General Wigner-Type Matrices.” Probability Theory and Related Fields. Springer, 2017. https://doi.org/10.1007/s00440-016-0740-2.","ista":"Ajanki OH, Erdös L, Krüger TH. 2017. Universality for general Wigner-type matrices. Probability Theory and Related Fields. 169(3–4), 667–727."},"user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","scopus_import":"1","intvolume":" 169","month":"12","abstract":[{"lang":"eng","text":"We consider the local eigenvalue distribution of large self-adjoint N×N random matrices H=H∗ with centered independent entries. In contrast to previous works the matrix of variances sij=\\mathbbmE|hij|2 is not assumed to be stochastic. Hence the density of states is not the Wigner semicircle law. Its possible shapes are described in the companion paper (Ajanki et al. in Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We show that as N grows, the resolvent, G(z)=(H−z)−1, converges to a diagonal matrix, diag(m(z)), where m(z)=(m1(z),…,mN(z)) solves the vector equation −1/mi(z)=z+∑jsijmj(z) that has been analyzed in Ajanki et al. (Quadratic Vector Equations on the Complex Upper Half Plane. arXiv:1506.05095). We prove a local law down to the smallest spectral resolution scale, and bulk universality for both real symmetric and complex hermitian symmetry classes."}],"oa_version":"Published Version","ec_funded":1,"volume":169,"issue":"3-4","publication_status":"published","publication_identifier":{"issn":["01788051"]},"language":[{"iso":"eng"}],"file":[{"file_name":"IST-2017-657-v1+2_s00440-016-0740-2.pdf","date_created":"2018-12-12T10:08:25Z","file_size":988843,"date_updated":"2020-07-14T12:44:44Z","creator":"system","checksum":"29f5a72c3f91e408aeb9e78344973803","file_id":"4686","content_type":"application/pdf","relation":"main_file","access_level":"open_access"}],"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)"},"type":"journal_article","pubrep_id":"657","status":"public","_id":"1337","file_date_updated":"2020-07-14T12:44:44Z","department":[{"_id":"LaEr"}],"date_updated":"2023-09-20T11:14:17Z","ddc":["510","530"]}]