Local uniformity properties for glauber dynamics on graph colorings

We investigate some local properties which hold with high probability for randomly selected colorings of a fixed graph with no short cycles. In a number of related works, establishing these particular properties has been a crucial step towards proving rapid convergence for the single-site Glauber dynamics, a Markov chain for sampling colorings uniformly at random. For a large class of graphs, this approach yields the most efficient known algorithms for sampling random colorings.