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

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• Andreas Galanis (Oxford)
• Tuesday 10 October 2023, 14:00-15:00
• MR12, Centre for Mathematical Sciences.

If you have a question about this talk, please contact Perla Sousi.

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.

This talk is part of the Probability series.

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