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
TypeArticle accepté pour publication ou publié
Journal nameAnnals of Probability
Institute of Mathematical Statistics
478 - 494
MetadataShow full item record
Abstract (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.
Subjects / KeywordsCutoff phenomenon; Exclusion process; mixing time; Negative dependence
Showing items related by title and author.