Glauber-Exclusion dynamics : rapid mixing regime

Ryokichi Tanaka; Kenkichi Tsunoda

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arXiv · 2011.13158

Glauber-Exclusion dynamics : rapid mixing regime

Ryokichi Tanaka·Kenkichi Tsunoda

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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).

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Ryokichi Tanaka, Kenkichi Tsunoda. 2020-11-26. Glauber-Exclusion dynamics : rapid mixing regime. https://arxiv.org/abs/2011.13158

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