A short note on mixing time of Glauber dynamics

Abstract

In this work we prove sufficient conditions for the Glauber dynamics corresponding to a sequence of (non-product) measures on finite product spaces to be rapidly mixing, i.e. that the mixing time with respect to the total variation distance satisfies \(t_{mix} = O(N \log N)\), where \(N\) is the system size. We apply this result to exponential random graph models with sufficiently small parameters. This does not require any monotonicity in the system and thus also applies to negative parameters, as long the associated monotone system is in the high temperature phase.