Glauber-Exclusion dynamics : rapid mixing regime

Ryokichi Tanaka, Kenkichi Tsunoda

Published 2020-11-26Version 1

We show that for any attractive Glauber-Exclusion process on the one-dimensional lattice of size $N$ with periodic boundary condition, if the corresponding hydrodynamic limit equation has a reaction term with a strictly convex potential, then the total-variation mixing time is of order $\Theta(\log N)$. In particular, the result covers the full high-temperature regime in the original model introduced by De Masi, Ferrari and Lebowitz (1985).