The Simple Exclusion Process on the Circle has a diffusive Cutoff Window

2014/01/28 by Lacoin, Hubert · 1 citation
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1401.7296

Abstract

In this paper, we investigate the mixing time of the simple exclusion process on the circle with N sites, with a number of particle k(N) tending to infinity, both from the worst initial condition and from a typical initial condition. We show that the worst-case mixing time is asymptotically equivalent to (8π²)^-1N²log k, while the cutoff window, is identified to be N². Starting from a typical condition, we show that there is no cutoff and that the mixing time is of order N².

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• Cylindric growth diagrams, walks in simplices, and exclusion processes

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