{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,17]],"date-time":"2025-09-17T04:40:52Z","timestamp":1758084052597,"version":"3.44.0"},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T00:00:00Z","timestamp":1752192000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We prove a Poisson process approximation result for stabilising functionals of a determinantal point process. Our results use concrete couplings of determinantal processes with different Palm measures and exploit their association properties. Second, we focus on the Ginibre process and show in the asymptotic scenario of an increasing observation window that the process of points with a large nearest neighbour distance converges after a suitable scaling to a Poisson point process. As a corollary, we obtain the scaling of the maximum nearest neighbour distance in the Ginibre process, which turns out to be different from its analogue for independent points.<\/jats:p>","DOI":"10.1017\/s0963548325000082","type":"journal-article","created":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T07:11:16Z","timestamp":1752217876000},"page":"635-648","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Couplings and Poisson approximation for stabilising functionals of determinantal point processes"],"prefix":"10.1017","volume":"34","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-6146-3975","authenticated-orcid":false,"given":"Moritz","family":"Otto","sequence":"first","affiliation":[{"name":"Aarhus University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2025,7,11]]},"reference":[{"key":"S0963548325000082_ref23","first-page":"1","article-title":"Extremal behavior of large cells in the Poisson hyperplane mosaic","volume":"162","author":"Otto","year":"2023","journal-title":"Electron. 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(2023) Compound Poisson process approximation under $\\beta$ -mixing and stabilization, Preprint, arXiv: 2310.15009."},{"key":"S0963548325000082_ref11","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-03-00975-3"},{"key":"S0963548325000082_ref15","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(92)90386-O"},{"key":"S0963548325000082_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-41598-7"},{"key":"S0963548325000082_ref9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-05233-5_10"},{"key":"S0963548325000082_ref17","doi-asserted-by":"publisher","DOI":"10.1017\/jpr.2019.10"},{"key":"S0963548325000082_ref2","volume-title":"Zeros of Gaussian Analytic Functions and Determinantal Point Processes","volume":"51","author":"Hough","year":"2009"},{"key":"S0963548325000082_ref18","doi-asserted-by":"publisher","DOI":"10.1214\/ECP.v4-1005"},{"key":"S0963548325000082_ref19","unstructured":"[19] Lyons, R. (2014) Determinantal probability: basic properties and conjectures, Preprint, arXiv: 1406.2707."},{"key":"S0963548325000082_ref10","doi-asserted-by":"publisher","DOI":"10.1214\/15-AOP1020"},{"key":"S0963548325000082_ref24","doi-asserted-by":"publisher","DOI":"10.3150\/23-BEJ1688"},{"key":"S0963548325000082_ref28","doi-asserted-by":"publisher","DOI":"10.1070\/RM2000v055n05ABEH000321"},{"key":"S0963548325000082_ref22","doi-asserted-by":"publisher","DOI":"10.1017\/jpr.2020.101"},{"key":"S0963548325000082_ref5","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176989121"},{"key":"S0963548325000082_ref26","doi-asserted-by":"publisher","DOI":"10.1016\/j.spl.2018.12.007"},{"key":"S0963548325000082_ref27","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-1236(03)00171-X"},{"key":"S0963548325000082_ref13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4015-8"},{"key":"S0963548325000082_ref7","doi-asserted-by":"publisher","DOI":"10.1007\/s10687-021-00430-6"},{"key":"S0963548325000082_ref16","doi-asserted-by":"publisher","DOI":"10.1214\/22-AAP1916"},{"key":"S0963548325000082_ref1","first-page":"206","article-title":"Determinantal Processes and Independence","volume":"3","author":"Hough","year":"2006","journal-title":"Probab. 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Published by Cambridge University Press","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}