[{"ddc":["510"],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"date_created":"2026-03-02T10:05:23Z","type":"journal_article","publication":"Probability Theory and Related Fields","abstract":[{"lang":"eng","text":"We study a (1 + 1)-dimensional semi-discrete random variational problem that can be interpreted as the geometrically linearized version of the critical 2-dimensional random field Ising model. The scaling of the correlation length of the latter was recently characterized in Probab. Duke Math. J. 172(9), 1781–1811 (2023) and arXiv:2011.08768v3, (2022); our analysis is reminiscent of the multi-scale approach of the latter work and of Combinatorica 9, 161–187 (1989) . We show that at every dyadic scale from the system size down to the lattice spacing the minimizer contains at most order-one Dirichlet energy per unit length. We also establish a quenched homogenization result in the sense that the leading order of the minimal energy becomes deterministic as the ratio system size / lattice spacing diverges. To this purpose we adapt arguments from arXiv:2401.06768, (2024) on the (d + 1)-dimensional version our the model, with a Brownian replacing the white noise potential, to obtain the initial large-scale bounds. Based on our estimate of the (p = 3)-Dirichlet energy, we give an informal justification of the geometric linearization. Our bounds, which are oblivious to the microscopic cut-off scale provided by the lattice spacing, yield tightness of the law of minimizers in the space of continuous functions as the lattice spacing is sent to zero."}],"publication_status":"epub_ahead","article_type":"original","citation":{"apa":"Otto, F., Palmieri, M., &#38; Wagner, C. (2026). On minimizing curves in a Brownian potential. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-026-01468-y\">https://doi.org/10.1007/s00440-026-01468-y</a>","chicago":"Otto, Felix, Matteo Palmieri, and Christian Wagner. “On Minimizing Curves in a Brownian Potential.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2026. <a href=\"https://doi.org/10.1007/s00440-026-01468-y\">https://doi.org/10.1007/s00440-026-01468-y</a>.","ista":"Otto F, Palmieri M, Wagner C. 2026. On minimizing curves in a Brownian potential. Probability Theory and Related Fields.","mla":"Otto, Felix, et al. “On Minimizing Curves in a Brownian Potential.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2026, doi:<a href=\"https://doi.org/10.1007/s00440-026-01468-y\">10.1007/s00440-026-01468-y</a>.","ieee":"F. Otto, M. Palmieri, and C. Wagner, “On minimizing curves in a Brownian potential,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2026.","short":"F. Otto, M. Palmieri, C. Wagner, Probability Theory and Related Fields (2026).","ama":"Otto F, Palmieri M, Wagner C. On minimizing curves in a Brownian potential. <i>Probability Theory and Related Fields</i>. 2026. doi:<a href=\"https://doi.org/10.1007/s00440-026-01468-y\">10.1007/s00440-026-01468-y</a>"},"publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"date_updated":"2026-03-02T15:15:13Z","_id":"21379","year":"2026","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","title":"On minimizing curves in a Brownian potential","author":[{"last_name":"Otto","full_name":"Otto, Felix","first_name":"Felix"},{"last_name":"Palmieri","full_name":"Palmieri, Matteo","first_name":"Matteo"},{"id":"bf0c729b-2619-11f0-8024-9d69bb2b8b20","first_name":"Christian","full_name":"Wagner, Christian","last_name":"Wagner"}],"acknowledgement":"FO and CW thank Ron Peled for insightful discussions on the white-noise multi-dimensional case in the Fall of 2023. CW thanks Barbara Dembin for the discussion during a workshop in Spring 2025. The work was done while the authors were affiliated with the Max Planck Institute for Mathematics in the Sciences; CW thanks the MPI for the support and warm hospitality. Open access funding provided by Institute of Science and Technology (IST Austria).","corr_author":"1","date_published":"2026-02-14T00:00:00Z","OA_type":"hybrid","oa":1,"oa_version":"Published Version","department":[{"_id":"JuFi"}],"quality_controlled":"1","status":"public","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00440-026-01468-y"}],"day":"14","has_accepted_license":"1","OA_place":"publisher","doi":"10.1007/s00440-026-01468-y","month":"02"},{"doi":"10.1007/s00440-025-01373-w","month":"12","file_date_updated":"2025-12-30T13:10:05Z","PlanS_conform":"1","day":"01","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"scopus_import":"1","OA_place":"publisher","has_accepted_license":"1","oa":1,"OA_type":"hybrid","external_id":{"isi":["001466997300001"],"arxiv":["2307.07432"]},"date_published":"2025-12-01T00:00:00Z","department":[{"_id":"LaEr"}],"oa_version":"Published Version","quality_controlled":"1","status":"public","arxiv":1,"page":"1183-1237","author":[{"full_name":"Riabov, Volodymyr","last_name":"Riabov","first_name":"Volodymyr","id":"1949f904-edfb-11eb-afb5-e2dfddabb93b"}],"corr_author":"1","acknowledgement":"I would like to express my gratitude to László Erdős for his careful guidance and supervision of my work. I am also thankful to Jana Reker and Joscha Henheik for many helpful discussions. Open access funding provided by Institute of Science and Technology (IST Austria).","isi":1,"intvolume":"       193","year":"2025","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","title":"Linear Eigenvalue statistics at the cusp","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"citation":{"ama":"Riabov V. Linear Eigenvalue statistics at the cusp. <i>Probability Theory and Related Fields</i>. 2025;193:1183-1237. doi:<a href=\"https://doi.org/10.1007/s00440-025-01373-w\">10.1007/s00440-025-01373-w</a>","ieee":"V. Riabov, “Linear Eigenvalue statistics at the cusp,” <i>Probability Theory and Related Fields</i>, vol. 193. Springer Nature, pp. 1183–1237, 2025.","short":"V. Riabov, Probability Theory and Related Fields 193 (2025) 1183–1237.","ista":"Riabov V. 2025. Linear Eigenvalue statistics at the cusp. Probability Theory and Related Fields. 193, 1183–1237.","mla":"Riabov, Volodymyr. “Linear Eigenvalue Statistics at the Cusp.” <i>Probability Theory and Related Fields</i>, vol. 193, Springer Nature, 2025, pp. 1183–237, doi:<a href=\"https://doi.org/10.1007/s00440-025-01373-w\">10.1007/s00440-025-01373-w</a>.","chicago":"Riabov, Volodymyr. “Linear Eigenvalue Statistics at the Cusp.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00440-025-01373-w\">https://doi.org/10.1007/s00440-025-01373-w</a>.","apa":"Riabov, V. (2025). Linear Eigenvalue statistics at the cusp. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-025-01373-w\">https://doi.org/10.1007/s00440-025-01373-w</a>"},"_id":"19598","date_updated":"2026-04-07T12:32:19Z","volume":193,"publication":"Probability Theory and Related Fields","publication_status":"published","article_type":"original","abstract":[{"text":"We establish universal Gaussian fluctuations for the mesoscopic linear eigenvalue statistics in the vicinity of the cusp-like singularities of the limiting spectral density for Wigner-type random matrices. Prior to this work, the linear eigenvalue statistics at the cusp-like singularities were not studied in any ensemble. Our analysis covers not only the exact cusps but the entire transitionary regime from the square-root singularity at a regular edge through the sharp cusp to the bulk. We identify a new one-parameter family of functionals that govern the limiting bias and variance, continuously interpolating between the previously known formulas in the bulk and at a regular edge. Since cusps are the only possible singularities besides the regular edges, our result gives a complete description of the linear eigenvalue statistics in all regimes.","lang":"eng"}],"ddc":["510"],"file":[{"date_updated":"2025-12-30T13:10:05Z","date_created":"2025-12-30T13:10:05Z","content_type":"application/pdf","creator":"dernst","checksum":"700229b280725c0d6aad0d71362cce5f","file_name":"2025_ProbTheoryRelatFields_Riabov.pdf","file_id":"20916","access_level":"open_access","file_size":919213,"relation":"main_file","success":1}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"related_material":{"record":[{"id":"20575","relation":"dissertation_contains","status":"public"}]},"type":"journal_article","date_created":"2025-04-20T22:01:28Z"},{"oa":1,"OA_type":"hybrid","date_published":"2025-01-01T00:00:00Z","project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"external_id":{"isi":["001493091900001"]},"quality_controlled":"1","status":"public","department":[{"_id":"LaEr"}],"oa_version":"Published Version","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Supported by ERC Advanced Grant “RMTBeyond” No. 101020331.","corr_author":"1","author":[{"first_name":"Giorgio","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Hong Chang","last_name":"Ji","full_name":"Ji, Hong Chang"}],"isi":1,"doi":"10.1007/s00440-025-01384-7","month":"01","day":"01","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00440-025-01384-7"}],"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"OA_place":"publisher","publication":"Probability Theory and Related Fields","article_number":"050603","article_type":"original","publication_status":"epub_ahead","abstract":[{"lang":"eng","text":"For general large non–Hermitian random matrices X and deterministic normal deformations A, we prove that the local eigenvalue statistics of A + X close to the critical edge points of its spectrum are universal. This concludes the proof of the third and last remaining typical universality class for non–Hermitian random matrices (for normal deformations), after bulk and sharp edge universalities have been established in recent years."}],"ddc":["500"],"type":"journal_article","date_created":"2025-05-25T22:16:59Z","year":"2025","ec_funded":1,"title":"Non–Hermitian spectral universality at critical points","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"citation":{"chicago":"Cipolloni, Giorgio, László Erdös, and Hong Chang Ji. “Non–Hermitian Spectral Universality at Critical Points.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00440-025-01384-7\">https://doi.org/10.1007/s00440-025-01384-7</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Ji, H. C. (2025). Non–Hermitian spectral universality at critical points. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-025-01384-7\">https://doi.org/10.1007/s00440-025-01384-7</a>","short":"G. Cipolloni, L. Erdös, H.C. Ji, Probability Theory and Related Fields (2025).","ieee":"G. Cipolloni, L. Erdös, and H. C. Ji, “Non–Hermitian spectral universality at critical points,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025.","mla":"Cipolloni, Giorgio, et al. “Non–Hermitian Spectral Universality at Critical Points.” <i>Probability Theory and Related Fields</i>, 050603, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00440-025-01384-7\">10.1007/s00440-025-01384-7</a>.","ista":"Cipolloni G, Erdös L, Ji HC. 2025. Non–Hermitian spectral universality at critical points. Probability Theory and Related Fields., 050603.","ama":"Cipolloni G, Erdös L, Ji HC. Non–Hermitian spectral universality at critical points. <i>Probability Theory and Related Fields</i>. 2025. doi:<a href=\"https://doi.org/10.1007/s00440-025-01384-7\">10.1007/s00440-025-01384-7</a>"},"_id":"19737","date_updated":"2026-06-18T18:17:57Z"},{"year":"2025","title":"Decorrelation transition in the Wigner minor process","ec_funded":1,"publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"citation":{"chicago":"Bao, Zhigang, Giorgio Cipolloni, László Erdös, Sven Joscha Henheik, and Oleksii Kolupaiev. “Decorrelation Transition in the Wigner Minor Process.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025. <a href=\"https://doi.org/10.1007/s00440-025-01422-4\">https://doi.org/10.1007/s00440-025-01422-4</a>.","apa":"Bao, Z., Cipolloni, G., Erdös, L., Henheik, S. J., &#38; Kolupaiev, O. (2025). Decorrelation transition in the Wigner minor process. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-025-01422-4\">https://doi.org/10.1007/s00440-025-01422-4</a>","ieee":"Z. Bao, G. Cipolloni, L. Erdös, S. J. Henheik, and O. Kolupaiev, “Decorrelation transition in the Wigner minor process,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2025.","short":"Z. Bao, G. Cipolloni, L. Erdös, S.J. Henheik, O. Kolupaiev, Probability Theory and Related Fields (2025).","mla":"Bao, Zhigang, et al. “Decorrelation Transition in the Wigner Minor Process.” <i>Probability Theory and Related Fields</i>, Springer Nature, 2025, doi:<a href=\"https://doi.org/10.1007/s00440-025-01422-4\">10.1007/s00440-025-01422-4</a>.","ista":"Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. 2025. Decorrelation transition in the Wigner minor process. Probability Theory and Related Fields.","ama":"Bao Z, Cipolloni G, Erdös L, Henheik SJ, Kolupaiev O. Decorrelation transition in the Wigner minor process. <i>Probability Theory and Related Fields</i>. 2025. doi:<a href=\"https://doi.org/10.1007/s00440-025-01422-4\">10.1007/s00440-025-01422-4</a>"},"_id":"20478","date_updated":"2026-06-18T18:23:40Z","publication":"Probability Theory and Related Fields","article_type":"original","publication_status":"epub_ahead","abstract":[{"text":"We consider the Wigner minor process, i.e. the eigenvalues of an N\\times N Wigner matrix H^{(N)} together with the eigenvalues of all its n\\times n minors, H^{(n)}, n\\le N. The top eigenvalues of H^{(N)} and those of its immediate minor H^{(N-1)} are very strongly correlated, but this correlation becomes weaker for smaller minors H^{(N-k)} as k increases. For the GUE minor process the critical transition regime around k\\sim N^{2/3} was analyzed by Forrester and Nagao (J. Stat. Mech.: Theory and Experiment, 2011) providing an explicit formula for the nontrivial joint correlation function. We prove that this formula is universal, i.e. it holds for the Wigner minor process. Moreover, we give a complete analysis of the sub- and supercritical regimes both for eigenvalues and for the corresponding eigenvector overlaps, thus we prove the decorrelation transition in full generality.","lang":"eng"}],"ddc":["500"],"type":"journal_article","date_created":"2025-10-16T13:10:26Z","doi":"10.1007/s00440-025-01422-4","month":"09","PlanS_conform":"1","day":"20","main_file_link":[{"open_access":"1","url":"https://doi.org/10.1007/s00440-025-01422-4"}],"scopus_import":"1","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"OA_place":"publisher","OA_type":"hybrid","oa":1,"date_published":"2025-09-20T00:00:00Z","external_id":{"isi":["001574640900001"],"arxiv":["2503.06549"]},"project":[{"_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020","grant_number":"101020331"}],"status":"public","quality_controlled":"1","oa_version":"Published Version","department":[{"_id":"LaEr"}],"arxiv":1,"corr_author":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria). Zhigang Bao Supported by Hong Kong RGC Grant GRF 16304724, NSFC12222121 and NSFC12271475. László Erdős, Joscha Henheik and Oleksii Kolupaiev Supported by the ERC Advanced Grant “RMTBeyond” No. 101020331.","author":[{"id":"442E6A6C-F248-11E8-B48F-1D18A9856A87","first_name":"Zhigang","orcid":"0000-0003-3036-1475","last_name":"Bao","full_name":"Bao, Zhigang"},{"orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"first_name":"László","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0003-1106-327X","last_name":"Henheik","full_name":"Henheik, Sven Joscha","first_name":"Sven Joscha","id":"31d731d7-d235-11ea-ad11-b50331c8d7fb"},{"first_name":"Oleksii","last_name":"Kolupaiev","full_name":"Kolupaiev, Oleksii","orcid":"0000-0003-1491-4623","id":"149b70d4-896a-11ed-bdf8-8c63fd44ca61"}],"isi":1},{"publisher":"Springer Nature","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","ec_funded":1,"title":"The critical variational setting for stochastic evolution equations","year":"2024","date_updated":"2025-09-04T11:27:46Z","_id":"12485","citation":{"ama":"Agresti A, Veraar M. The critical variational setting for stochastic evolution equations. <i>Probability Theory and Related Fields</i>. 2024;188:957-1015. doi:<a href=\"https://doi.org/10.1007/s00440-023-01249-x\">10.1007/s00440-023-01249-x</a>","mla":"Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for Stochastic Evolution Equations.” <i>Probability Theory and Related Fields</i>, vol. 188, Springer Nature, 2024, pp. 957–1015, doi:<a href=\"https://doi.org/10.1007/s00440-023-01249-x\">10.1007/s00440-023-01249-x</a>.","ista":"Agresti A, Veraar M. 2024. The critical variational setting for stochastic evolution equations. Probability Theory and Related Fields. 188, 957–1015.","short":"A. Agresti, M. Veraar, Probability Theory and Related Fields 188 (2024) 957–1015.","ieee":"A. Agresti and M. Veraar, “The critical variational setting for stochastic evolution equations,” <i>Probability Theory and Related Fields</i>, vol. 188. Springer Nature, pp. 957–1015, 2024.","apa":"Agresti, A., &#38; Veraar, M. (2024). The critical variational setting for stochastic evolution equations. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-023-01249-x\">https://doi.org/10.1007/s00440-023-01249-x</a>","chicago":"Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for Stochastic Evolution Equations.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00440-023-01249-x\">https://doi.org/10.1007/s00440-023-01249-x</a>."},"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"abstract":[{"lang":"eng","text":"In this paper we introduce the critical variational setting for parabolic stochastic evolution equations of quasi- or semi-linear type. Our results improve many of the abstract results in the classical variational setting. In particular, we are able to replace the usual weak or local monotonicity condition by a more flexible local Lipschitz condition. Moreover, the usual growth conditions on the multiplicative noise are weakened considerably. Our new setting provides general conditions under which local and global existence and uniqueness hold. Moreover, we prove continuous dependence on the initial data. We show that many classical SPDEs, which could not be covered by the classical variational setting, do fit in the critical variational setting. In particular, this is the case for the Cahn-Hilliard equations, tamed Navier-Stokes equations, and Allen-Cahn equation."}],"publication_status":"published","article_type":"original","publication":"Probability Theory and Related Fields","volume":188,"date_created":"2023-02-02T10:45:15Z","type":"journal_article","ddc":["510"],"file":[{"file_id":"17296","file_name":"2024_ProbTheory_Agresti.pdf","checksum":"b8572339dbc5b8de4934dc5fd34afc7d","success":1,"relation":"main_file","file_size":942801,"access_level":"open_access","content_type":"application/pdf","date_created":"2024-07-22T09:21:09Z","date_updated":"2024-07-22T09:21:09Z","creator":"dernst"}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file_date_updated":"2024-07-22T09:21:09Z","month":"04","doi":"10.1007/s00440-023-01249-x","has_accepted_license":"1","article_processing_charge":"Yes (in subscription journal)","language":[{"iso":"eng"}],"scopus_import":"1","day":"01","oa_version":"Published Version","department":[{"_id":"JuFi"}],"quality_controlled":"1","status":"public","project":[{"grant_number":"948819","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","name":"Bridging Scales in Random Materials","call_identifier":"H2020"}],"external_id":{"isi":["001154226500001"],"arxiv":["2206.00230"]},"date_published":"2024-04-01T00:00:00Z","oa":1,"isi":1,"intvolume":"       188","author":[{"id":"673cd0cc-9b9a-11eb-b144-88f30e1fbb72","first_name":"Antonio","orcid":"0000-0002-9573-2962","last_name":"Agresti","full_name":"Agresti, Antonio"},{"first_name":"Mark","full_name":"Veraar, Mark","last_name":"Veraar"}],"acknowledgement":"The first author has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 948819) . The second author is supported by the VICI subsidy VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).","page":"957-1015","arxiv":1},{"intvolume":"       188","isi":1,"acknowledgement":"The authors are grateful to Joscha Henheik for his help with the formulas in Appendix B.\r\nLászló Erdős supported by ERC Advanced Grant “RMTBeyond” No. 101020331. Dominik Schröder supported by the SNSF Ambizione Grant PZ00P2 209089.","author":[{"last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","orcid":"0000-0002-4901-7992","first_name":"Giorgio","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"orcid":"0000-0002-2904-1856","full_name":"Schröder, Dominik J","last_name":"Schröder","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"arxiv":1,"page":"1131-1182","status":"public","quality_controlled":"1","oa_version":"Preprint","department":[{"_id":"LaEr"}],"date_published":"2024-04-01T00:00:00Z","project":[{"grant_number":"101020331","_id":"62796744-2b32-11ec-9570-940b20777f1d","name":"Random matrices beyond Wigner-Dyson-Mehta","call_identifier":"H2020"}],"external_id":{"isi":["001118972500001"],"arxiv":["2210.12060"]},"oa":1,"scopus_import":"1","language":[{"iso":"eng"}],"article_processing_charge":"No","day":"01","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2210.12060"}],"month":"04","doi":"10.1007/s00440-023-01229-1","date_created":"2023-10-08T22:01:17Z","type":"journal_article","abstract":[{"lang":"eng","text":"We prove that the mesoscopic linear statistics ∑if(na(σi−z0)) of the eigenvalues {σi}i of large n×n non-Hermitian random matrices with complex centred i.i.d. entries are asymptotically Gaussian for any H20-functions f around any point z0 in the bulk of the spectrum on any mesoscopic scale 0<a<1/2. This extends our previous result (Cipolloni et al. in Commun Pure Appl Math, 2019. arXiv:1912.04100), that was valid on the macroscopic scale, a=0\r\n, to cover the entire mesoscopic regime. The main novelty is a local law for the product of resolvents for the Hermitization of X at spectral parameters z1,z2 with an improved error term in the entire mesoscopic regime |z1−z2|≫n−1/2. The proof is dynamical; it relies on a recursive tandem of the characteristic flow method and the Green function comparison idea combined with a separation of the unstable mode of the underlying stability operator."}],"article_type":"original","publication_status":"published","publication":"Probability Theory and Related Fields","volume":188,"date_updated":"2025-08-05T13:28:15Z","_id":"14408","citation":{"ama":"Cipolloni G, Erdös L, Schröder DJ. Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. 2024;188:1131-1182. doi:<a href=\"https://doi.org/10.1007/s00440-023-01229-1\">10.1007/s00440-023-01229-1</a>","mla":"Cipolloni, Giorgio, et al. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>, vol. 188, Springer Nature, 2024, pp. 1131–82, doi:<a href=\"https://doi.org/10.1007/s00440-023-01229-1\">10.1007/s00440-023-01229-1</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2024. Mesoscopic central limit theorem for non-Hermitian random matrices. Probability Theory and Related Fields. 188, 1131–1182.","short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 188 (2024) 1131–1182.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Mesoscopic central limit theorem for non-Hermitian random matrices,” <i>Probability Theory and Related Fields</i>, vol. 188. Springer Nature, pp. 1131–1182, 2024.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2024). Mesoscopic central limit theorem for non-Hermitian random matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-023-01229-1\">https://doi.org/10.1007/s00440-023-01229-1</a>","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Mesoscopic Central Limit Theorem for Non-Hermitian Random Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00440-023-01229-1\">https://doi.org/10.1007/s00440-023-01229-1</a>."},"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"ec_funded":1,"title":"Mesoscopic central limit theorem for non-Hermitian random matrices","publisher":"Springer Nature","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2024"},{"scopus_import":"1","language":[{"iso":"eng"}],"article_processing_charge":"Yes (in subscription journal)","day":"01","has_accepted_license":"1","OA_place":"publisher","doi":"10.1007/s00440-023-01254-0","file_date_updated":"2025-01-09T08:10:54Z","month":"10","acknowledgement":"NC has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No 948819).\r\nFM is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through the SPP 2265 Random Geometric Systems. FM has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044 -390685587, Mathematics Münster: Dynamics–Geometry–Structure. FM has been funded by the Max Planck Institute for Mathematics in the Sciences.","corr_author":"1","author":[{"last_name":"Clozeau","full_name":"Clozeau, Nicolas","first_name":"Nicolas","id":"fea1b376-906f-11eb-847d-b2c0cf46455b"},{"first_name":"Francesco","full_name":"Mattesini, Francesco","last_name":"Mattesini"}],"arxiv":1,"page":"485-541","intvolume":"       190","isi":1,"date_published":"2024-10-01T00:00:00Z","external_id":{"arxiv":["2303.00353"],"isi":["001136206200002"]},"project":[{"name":"Bridging Scales in Random Materials","call_identifier":"H2020","_id":"0aa76401-070f-11eb-9043-b5bb049fa26d","grant_number":"948819"}],"oa":1,"OA_type":"hybrid","quality_controlled":"1","status":"public","oa_version":"Published Version","department":[{"_id":"JuFi"}],"citation":{"chicago":"Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2024. <a href=\"https://doi.org/10.1007/s00440-023-01254-0\">https://doi.org/10.1007/s00440-023-01254-0</a>.","apa":"Clozeau, N., &#38; Mattesini, F. (2024). Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-023-01254-0\">https://doi.org/10.1007/s00440-023-01254-0</a>","short":"N. Clozeau, F. Mattesini, Probability Theory and Related Fields 190 (2024) 485–541.","ieee":"N. Clozeau and F. Mattesini, “Annealed quantitative estimates for the quadratic 2D-discrete random matching problem,” <i>Probability Theory and Related Fields</i>, vol. 190. Springer Nature, pp. 485–541, 2024.","mla":"Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates for the Quadratic 2D-Discrete Random Matching Problem.” <i>Probability Theory and Related Fields</i>, vol. 190, Springer Nature, 2024, pp. 485–541, doi:<a href=\"https://doi.org/10.1007/s00440-023-01254-0\">10.1007/s00440-023-01254-0</a>.","ista":"Clozeau N, Mattesini F. 2024. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. Probability Theory and Related Fields. 190, 485–541.","ama":"Clozeau N, Mattesini F. Annealed quantitative estimates for the quadratic 2D-discrete random matching problem. <i>Probability Theory and Related Fields</i>. 2024;190:485-541. doi:<a href=\"https://doi.org/10.1007/s00440-023-01254-0\">10.1007/s00440-023-01254-0</a>"},"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"date_updated":"2025-09-04T11:43:43Z","_id":"14797","year":"2024","ec_funded":1,"title":"Annealed quantitative estimates for the quadratic 2D-discrete random matching problem","user_id":"317138e5-6ab7-11ef-aa6d-ffef3953e345","publisher":"Springer Nature","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"file_size":880117,"success":1,"relation":"main_file","access_level":"open_access","file_id":"18788","checksum":"34f44cad6a210ff66791ee37e590af2c","file_name":"2024_ProbTheoryRelatFields_Clozeau.pdf","creator":"dernst","content_type":"application/pdf","date_updated":"2025-01-09T08:10:54Z","date_created":"2025-01-09T08:10:54Z"}],"ddc":["510"],"date_created":"2024-01-14T23:00:57Z","type":"journal_article","publication":"Probability Theory and Related Fields","volume":190,"abstract":[{"lang":"eng","text":"We study a random matching problem on closed compact  2 -dimensional Riemannian manifolds (with respect to the squared Riemannian distance), with samples of random points whose common law is absolutely continuous with respect to the volume measure with strictly positive and bounded density. We show that given two sequences of numbers  n  and  m=m(n)  of points, asymptotically equivalent as  n  goes to infinity, the optimal transport plan between the two empirical measures  μn  and  νm  is quantitatively well-approximated by  (Id,exp(∇hn))#μn  where  hn  solves a linear elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère equation. This is obtained in the case of samples of correlated random points for which a stretched exponential decay of the  α -mixing coefficient holds and for a class of discrete-time Markov chains having a unique absolutely continuous invariant measure with respect to the volume measure."}],"article_type":"original","publication_status":"published"},{"_id":"11741","date_updated":"2024-10-09T21:03:02Z","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"citation":{"short":"G. Cipolloni, L. Erdös, D.J. Schröder, Probability Theory and Related Fields 185 (2023) 1183–1218.","ieee":"G. Cipolloni, L. Erdös, and D. J. Schröder, “Quenched universality for deformed Wigner matrices,” <i>Probability Theory and Related Fields</i>, vol. 185. Springer Nature, pp. 1183–1218, 2023.","mla":"Cipolloni, Giorgio, et al. “Quenched Universality for Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>, vol. 185, Springer Nature, 2023, pp. 1183–1218, doi:<a href=\"https://doi.org/10.1007/s00440-022-01156-7\">10.1007/s00440-022-01156-7</a>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2023. Quenched universality for deformed Wigner matrices. Probability Theory and Related Fields. 185, 1183–1218.","chicago":"Cipolloni, Giorgio, László Erdös, and Dominik J Schröder. “Quenched Universality for Deformed Wigner Matrices.” <i>Probability Theory and Related Fields</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00440-022-01156-7\">https://doi.org/10.1007/s00440-022-01156-7</a>.","apa":"Cipolloni, G., Erdös, L., &#38; Schröder, D. J. (2023). Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00440-022-01156-7\">https://doi.org/10.1007/s00440-022-01156-7</a>","ama":"Cipolloni G, Erdös L, Schröder DJ. Quenched universality for deformed Wigner matrices. <i>Probability Theory and Related Fields</i>. 2023;185:1183–1218. doi:<a href=\"https://doi.org/10.1007/s00440-022-01156-7\">10.1007/s00440-022-01156-7</a>"},"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","publisher":"Springer Nature","title":"Quenched universality for deformed Wigner matrices","year":"2023","type":"journal_article","date_created":"2022-08-07T22:02:00Z","file":[{"file_id":"14054","file_name":"2023_ProbabilityTheory_Cipolloni.pdf","checksum":"b9247827dae5544d1d19c37abe547abc","relation":"main_file","success":1,"file_size":782278,"access_level":"open_access","content_type":"application/pdf","date_updated":"2023-08-14T12:47:32Z","date_created":"2023-08-14T12:47:32Z","creator":"dernst"}],"ddc":["510"],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"article_type":"original","publication_status":"published","abstract":[{"text":"Following E. Wigner’s original vision, we prove that sampling the eigenvalue gaps within the bulk spectrum of a fixed (deformed) Wigner matrix H yields the celebrated Wigner-Dyson-Mehta universal statistics with high probability. Similarly, we prove universality for a monoparametric family of deformed Wigner matrices H+xA with a deterministic Hermitian matrix A and a fixed Wigner matrix H, just using the randomness of a single scalar real random variable x. Both results constitute quenched versions of bulk universality that has so far only been proven in annealed sense with respect to the probability space of the matrix ensemble.","lang":"eng"}],"volume":185,"publication":"Probability Theory and Related Fields","has_accepted_license":"1","day":"01","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"scopus_import":"1","month":"04","file_date_updated":"2023-08-14T12:47:32Z","doi":"10.1007/s00440-022-01156-7","isi":1,"intvolume":"       185","arxiv":1,"page":"1183–1218","author":[{"id":"42198EFA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4901-7992","last_name":"Cipolloni","full_name":"Cipolloni, Giorgio","first_name":"Giorgio"},{"orcid":"0000-0001-5366-9603","last_name":"Erdös","full_name":"Erdös, László","first_name":"László","id":"4DBD5372-F248-11E8-B48F-1D18A9856A87"},{"id":"408ED176-F248-11E8-B48F-1D18A9856A87","full_name":"Schröder, Dominik J","last_name":"Schröder","orcid":"0000-0002-2904-1856","first_name":"Dominik J"}],"corr_author":"1","acknowledgement":"The authors are indebted to Sourav Chatterjee for forwarding the very inspiring question that Stephen Shenker originally addressed to him which initiated the current paper. They are also grateful that the authors of [23] kindly shared their preliminary numerical results in June 2021.\r\nOpen access funding provided by Institute of Science and Technology (IST Austria).","oa_version":"Published Version","department":[{"_id":"LaEr"}],"status":"public","quality_controlled":"1","oa":1,"external_id":{"arxiv":["2106.10200"],"isi":["000830344500001"]},"date_published":"2023-04-01T00:00:00Z"},{"status":"public","quality_controlled":"1","department":[{"_id":"LaEr"}],"oa_version":"Published Version","oa":1,"date_published":"2021-02-01T00:00:00Z","external_id":{"arxiv":["1908.00969"],"isi":["000572724600002"]},"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","call_identifier":"FP7","grant_number":"338804"},{"name":"International IST Doctoral Program","call_identifier":"H2020","_id":"2564DBCA-B435-11E9-9278-68D0E5697425","grant_number":"665385"}],"isi":1,"arxiv":1,"corr_author":"1","author":[{"first_name":"Giorgio","full_name":"Cipolloni, Giorgio","last_name":"Cipolloni","orcid":"0000-0002-4901-7992","id":"42198EFA-F248-11E8-B48F-1D18A9856A87"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0001-5366-9603","full_name":"Erdös, László","last_name":"Erdös","first_name":"László"},{"last_name":"Schröder","full_name":"Schröder, Dominik J","orcid":"0000-0002-2904-1856","first_name":"Dominik J","id":"408ED176-F248-11E8-B48F-1D18A9856A87"}],"month":"02","file_date_updated":"2020-10-05T14:53:40Z","doi":"10.1007/s00440-020-01003-7","has_accepted_license":"1","day":"01","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"article_type":"original","publication_status":"published","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"}],"publication":"Probability Theory and Related Fields","type":"journal_article","date_created":"2020-10-04T22:01:37Z","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"relation":"main_file","success":1,"file_size":497032,"access_level":"open_access","file_id":"8612","file_name":"2020_ProbTheory_Cipolloni.pdf","checksum":"611ae28d6055e1e298d53a57beb05ef4","creator":"dernst","content_type":"application/pdf","date_created":"2020-10-05T14:53:40Z","date_updated":"2020-10-05T14:53:40Z"}],"ddc":["510"],"ec_funded":1,"title":"Edge universality for non-Hermitian random matrices","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","publisher":"Springer Nature","year":"2021","_id":"8601","date_updated":"2026-04-02T14:03:52Z","publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"citation":{"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>","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>.","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>.","ista":"Cipolloni G, Erdös L, Schröder DJ. 2021. Edge universality for non-Hermitian random matrices. Probability Theory and Related Fields.","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,” <i>Probability Theory and Related Fields</i>. Springer Nature, 2021.","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>"}},{"year":"2019","title":"Singular SPDEs in domains with boundaries","publisher":"Springer","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","publication_identifier":{"issn":["0178-8051"],"eissn":["1432-2064"]},"citation":{"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>","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>.","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>.","ista":"Gerencser M, Hairer M. 2019. Singular SPDEs in domains with boundaries. Probability Theory and Related Fields. 173(3–4), 697–758.","short":"M. Gerencser, M. Hairer, Probability Theory and Related Fields 173 (2019) 697–758.","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."},"_id":"319","date_updated":"2026-04-03T09:45:34Z","volume":173,"publication":"Probability Theory and Related Fields","article_type":"original","publication_status":"published","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."}],"tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"file":[{"content_type":"application/pdf","date_updated":"2020-07-14T12:46:03Z","date_created":"2018-12-17T16:25:24Z","creator":"dernst","file_id":"5722","file_name":"2018_ProbTheory_Gerencser.pdf","checksum":"288d16ef7291242f485a9660979486e3","relation":"main_file","file_size":893182,"access_level":"open_access"}],"ddc":["510"],"type":"journal_article","date_created":"2018-12-11T11:45:48Z","doi":"10.1007/s00440-018-0841-1","month":"04","file_date_updated":"2020-07-14T12:46:03Z","day":"01","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"issue":"3-4","has_accepted_license":"1","oa":1,"date_published":"2019-04-01T00:00:00Z","publist_id":"7546","project":[{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"external_id":{"isi":["000463613800001"]},"status":"public","quality_controlled":"1","oa_version":"Published Version","department":[{"_id":"JaMa"}],"page":"697–758","acknowledgement":"MG thanks the support of the LMS Postdoctoral Mobility Grant.\r\n\r\n","corr_author":"1","author":[{"last_name":"Gerencser","full_name":"Gerencser, Mate","first_name":"Mate","id":"44ECEDF2-F248-11E8-B48F-1D18A9856A87"},{"first_name":"Martin","last_name":"Hairer","full_name":"Hairer, Martin"}],"intvolume":"       173","isi":1},{"intvolume":"       173","isi":1,"corr_author":"1","acknowledgement":"Open access funding provided by Institute of Science and Technology (IST Austria).\r\n","author":[{"id":"36F2FB7E-F248-11E8-B48F-1D18A9856A87","first_name":"Oskari H","full_name":"Ajanki, Oskari H","last_name":"Ajanki"},{"id":"4DBD5372-F248-11E8-B48F-1D18A9856A87","last_name":"Erdös","full_name":"Erdös, László","orcid":"0000-0001-5366-9603","first_name":"László"},{"id":"3020C786-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-4821-3297","full_name":"Krüger, Torben H","last_name":"Krüger","first_name":"Torben H"}],"page":"293–373","quality_controlled":"1","status":"public","oa_version":"Published Version","department":[{"_id":"LaEr"}],"date_published":"2019-02-01T00:00:00Z","external_id":{"isi":["000459396500007"]},"publist_id":"7394","project":[{"name":"Random matrices, universality and disordered quantum systems","call_identifier":"FP7","_id":"258DCDE6-B435-11E9-9278-68D0E5697425","grant_number":"338804"},{"_id":"B67AFEDC-15C9-11EA-A837-991A96BB2854","name":"IST Austria Open Access Fund"}],"oa":1,"has_accepted_license":"1","issue":"1-2","scopus_import":"1","article_processing_charge":"Yes (via OA deal)","language":[{"iso":"eng"}],"day":"01","file_date_updated":"2020-07-14T12:46:26Z","month":"02","doi":"10.1007/s00440-018-0835-z","date_created":"2018-12-11T11:46:25Z","type":"journal_article","tmp":{"short":"CC BY (4.0)","name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"ddc":["510"],"file":[{"file_size":1201840,"relation":"main_file","access_level":"open_access","file_id":"5720","checksum":"f9354fa5c71f9edd17132588f0dc7d01","file_name":"2018_ProbTheory_Ajanki.pdf","creator":"dernst","content_type":"application/pdf","date_updated":"2020-07-14T12:46:26Z","date_created":"2018-12-17T16:12:08Z"}],"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."}],"publication_status":"published","article_type":"original","publication":"Probability Theory and Related Fields","volume":173,"date_updated":"2026-04-03T09:46:51Z","_id":"429","citation":{"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>","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.","short":"O.H. Ajanki, L. Erdös, T.H. Krüger, Probability Theory and Related Fields 173 (2019) 293–373.","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.","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>"},"publication_identifier":{"eissn":["1432-2064"],"issn":["0178-8051"]},"ec_funded":1,"title":"Stability of the matrix Dyson equation and random matrices with correlations","publisher":"Springer","user_id":"ba8df636-2132-11f1-aed0-ed93e2281fdd","year":"2019"}]