A Note on the Glauber Dynamics for Sampling Independent Sets

This note considers the problem of sampling from the set of weighted independent sets of a graph with maximum degree ∆. For a positive fugacity λ, the weight of an independent set σ is λ|σ|. Luby and Vigoda proved that the Glauber dynamics, which only changes the configuration at a randomly chosen vertex in each step, has mixing time O(n log n) when λ < 2 ∆−2 for triangle-free graphs. We extend their approach to general graphs.