A note on the Glauber dynamics for sampling independent sets (Q1594581)

Summary: This note considers the problem of sampling from the set of\break weighted independent sets of a graph with maximum degree \(\Delta\). For a positive fugacity \(\lambda\), the weight of an independent set \(\sigma\) is \(\lambda^{|\sigma|}\). 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 \(\lambda<{{2}\over {\Delta-2}}\) for triangle-free graphs. We extend their approach to general graphs.