Relaxation to equilibrium of conservative dynamics. I: Zero-range processes (Q1807196)

The decay rate to equilibrium in the variance sense is derived for symmetric zero range processes in \(\mathbb{Z}^d\) under weak assumptions. For any local function \(u\) it is shown to be of the form \(C_ut^{-d/2}+ o(t^{-d/2})\). An explicit representation of \(C_u\) is given. Basic ingredients of the proof are the spectral gap for the processes on finite boxes and a Nash inequality.