Spectral gap for the zero range process with constant rate

Abstract

We solve an open problem concerning the relaxation time (inverse spectral gap) of the zero range process in ${\mathbf{Z}}^d/L{\mathbf{Z}}^d$ with constant rate, proving a tight upper bound of $O((\rho +1{)}^2{L}^2)$, where $\rho$ is the density of particles.

Published at http://dx.doi.org/10.1214/009117906000000304 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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