The joint mixing time of the random walk and dynamical random-cluster process is Θ(log n) when edge updates are fast enough in the subcritical regime on random regular graphs.
Mixing times of random walks on dynamic configuration models.The Annals of Applied Probability, 28(4):1977– 2002
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Logarithmic Mixing of Random Walks on Dynamical Random Cluster Models
The joint mixing time of the random walk and dynamical random-cluster process is Θ(log n) when edge updates are fast enough in the subcritical regime on random regular graphs.