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.
Cutoff for random walk on dynamical Erd ˝os–R´enyi graph.Annales de l’Institut Henri Poincar´e, Probabilit´es et Statistiques, 56(4), November 2020
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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.