Condensation of the invariant measures of the supercritical zero range processes

2020/07/12 by Xu, Tiecheng
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2007.06085

Abstract

For α≥ 1, let g:\mathbb N→\mathbb R₊ be given by g(0)=0, g(1)=1, g(k)=(k/k-1)^α, k≥ 2. Consider the symmetric nearest neighbour zero range process on the discrete torus \mathbb T_L in which a particle jumps from a site, occupied by k particles, to one of its neighbors with rate g(k). Armendáriz and Loulakis\citeal09 proved a strong form of the equivalence of ensembles for the invariant measure of the supercritical zero range process with α>2. We generalize their result to all α≥ 1.

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