Random-Cluster Dynamics on Random Regular Graphs in Tree Uniqueness

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

Keywords:

• Glauber
• Exponential function
• Regular graph
• Mixing (mathematics)
• tree
• Potts model
• Combinatorics
• Random graph
• Mathematics
• Uniqueness

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