Glauber-Exclusion dynamics : rapid mixing regime

TL;DR

This paper proves that certain one-dimensional Glauber-Exclusion processes with convex reaction potentials mix rapidly in logarithmic time, especially in the high-temperature regime, indicating efficient convergence to equilibrium.

Contribution

It establishes that attractive Glauber-Exclusion processes with convex reaction potentials have mixing times of order O(log N), covering the full high-temperature regime.

Findings

Mixing time is O(log N) for the specified processes.

Results apply to the full high-temperature regime.

The work connects hydrodynamic limits with rapid mixing behavior.

Abstract

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 $O(\log N)$. In particular, the result covers the full high-temperature regime in the original model introduced by De Masi, Ferrari and Lebowitz (1985).