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.
Ann. Probab.
24(4):
1871-1902
(October 1996).
DOI: 10.1214/aop/1041903209