Condensation of the invariant measures of the supercritical zero range processes

Abstract

For $\alpha \ge 1$, let $g:\mathbb{N}\to {\mathbb{R}}_{+}$ be given by $g(0)=0$, $g(1)=1$, $g(k)=(k/k-1{)}^{\alpha }$, $k\ge 2$. 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\cite{al09} proved a strong form of the equivalence of ensembles for the invariant measure of the supercritical zero range process with $\alpha >2$. We generalize their result to all $\alpha \ge 1$.

13 pages

References in corpus (1)

• Condensation for a fixed number of independent random variables