Lower bound estimate of the spectral gap for simple exclusion process with degenerate rates

Abstract

We consider exclusion process with degenerate rates in a finite torus with size $n$. This model is a simplified model for some peculiar phenomena of the "glassy" dynamics. We prove that the spectral gap is bounded below by $C\rho^4/n^2$, where $\rho = k/n$ denotes the density of particle and $C$ does not depend on $n$ nor $\rho$.