Random-Cluster Dynamics on Random Regular Graphs in Tree Uniqueness
2021
We establish rapid mixing of the random-cluster Glauber dynamics on random $$\varDelta $$
-regular graphs for all $$q\ge 1$$
and $$p2$$
the Glauber dynamics on random $$\varDelta $$
-regular graphs undergoes an exponential slowdown at $$p_u(q,\varDelta )$$
. More precisely, we show that for every $$q\ge 1$$
, $$\varDelta \ge 3$$
, and $$p
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