Home / Events / Sampling from the random cluster model on the random regular graph at all temperatures
Probability Seminars

Sampling from the random cluster model on the random regular graph at all temperatures

With Andreas Galanis (Oxford)

Sampling from the random cluster model on the random regular graph at all temperatures

We consider the performance of Glauber dynamics for the random cluster model (with q>1). On the random regular graph, the model exhibits the ordered/disordered transition which causes bottlenecks in an interval of temperatures (for q>2). This impedes fast mixing from worst-case starting configurations, for both local and non-local Markov chains. Nevertheless, it is widely conjectured that the bottlenecks can be avoided by initialising the chain more judiciously.

Our main result establishes this conjecture for all sufficiently large q (with respect to the degree Δ). Specifically, we consider the mixing time of Glauber dynamics initialised from the two extreme configurations, and obtain a pair of fast mixing bounds which cover all temperatures, including in particular the bottleneck window.

Joint with L. Goldberg and P. Smolarova.

Add to your calendar or Include in your list