Spectral gap for zero-range dynamics

Abstract

We give a lower bound on the spectral gap for symmetric zero-range processes. Under some conditions on the rate function, we show that the gap shrinks as $n^{-2}$, independent of the density, for the dynamics localized on a cube of size $n^d$. We follow the method outlined by Lu and Yau, where a similar spectral gap is proved for Kawasaki dynamics.