Universality of cutoff for exclusion with reservoirs
Salez, Justin (2023), Universality of cutoff for exclusion with reservoirs, Annals of Probability, 51, 2, p. 478 - 494. 10.1214/22-AOP1600
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Type
Article accepté pour publication ou publiéDate
2023Nom de la revue
Annals of ProbabilityVolume
51Numéro
2Éditeur
Institute of Mathematical Statistics
Ville d’édition
Paris
Pages
478 - 494
Identifiant publication
Métadonnées
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Salez, JustinRésumé (EN)
We consider the exclusion process with reservoirs on arbitrary networks. We characterize the spectral gap, mixing time, and mixing window of the process, in terms of certain simple spectral statistics of the underlying network. Among other consequences we establish a nonconservative analogue of Aldous’s spectral gap conjecture, and we show that cutoff occurs if and only if the product condition is satisfied. We illustrate this by providing explicit cutoffs on discrete lattices of arbitrary dimensions and boundary conditions which substantially generalize recent one-dimensional results. We also obtain cutoff phenomena in relative entropy, Hilbert norm, separation distance, and supremum norm. Our proof exploits negative dependence in a novel, simple way to reduce the understanding of the whole process to that of single-site marginals. We believe that this approach will find other applications.Mots-clés
Cutoff phenomenon; Exclusion process; mixing time; Negative dependencePublications associées
Affichage des éléments liés par titre et auteur.
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Tran, Hong-Quan (2022) Document de travail / Working paper
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Xu, Lu (2022) Article accepté pour publication ou publié
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Caputo, Pietro; Labbé, Cyril; Lacoin, Hubert (2022) Article accepté pour publication ou publié
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Bristiel, Alexandre; Salez, Justin (2022) Document de travail / Working paper
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Salez, Justin (2021) Document de travail / Working paper