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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

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Type
Article accepté pour publication ou publié
Date
2011
Journal name
Alea
Volume
8
Number
1
Pages
285-301
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Author(s)
Lacoin, Hubert
Leblond, Rémi
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 / Keywords
Mixing Time; Cutoff; Exclusion Process