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.
Limit theory for random walks in degenerate time- dependent random environments.Journal of Functional Analysis, 274(4):985–1046
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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.