Cutoff phenomenon for the simple exclusion process on the complete graph

Abstract

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 (n/2)\log \min(k, \sqrt{n}), and that around this time, for any small positive epsilon the total variation distance drops from 1-epsilon to epsilon 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.

16 pages, to appear in ALEA

References in corpus (3)

• The mixing time evolution of Glauber dynamics for the mean-field Ising model
• Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk
• Mixing times for random k-cycles and coalescence-fragmentation chains

Cited by in corpus (5)

• The cutoff profile for the simple exclusion process on the circle
• Mixing time and cutoff for the adjacent transposition shuffle and the simple exclusion
• Mixing of the Averaging process and its discrete dual on finite-dimensional geometries
• Partial mixing of semi-random transposition shuffles
• The cutoff profile for exclusion processes in any dimension