Cutoff phenomenon for the simple exclusion process on the complete graph
Lacoin, Hubert; Leblond, Rémi (2011), Cutoff phenomenon for the simple exclusion process on the complete graph, Alea, 8, 1, p. 285-301
TypeArticle accepté pour publication ou publié
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Abstract (EN)We study the time that the simple exclusion process on the complete graph needs to reach equilibrium in terms of total variation distance. For the graph with n vertices and 1 ≪ k < n/2 particles, we show that the mixing time is of order 1 2n logmin(k,√n), and that around this time, for any ", the total variation distance drops from 1 − " to " in a time window whose width is of order n (i.e. in a much shorter time). Our proof is purely probabilistic and self-contained.
Subjects / KeywordsMixing Time; Cutoff; Exclusion Process
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