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Mixing time of random walk on dynamical random cluster

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We consider a random walk jumping on a dynamic graph (that is, the graph changes at the same time as the walker moves) given by Glauber dynamics on the random cluster model. In this model, the edges of the graph change their state, between open and closed, via a dynamics with unbounded dependences. We derive tight bounds on the mixing time when the density of open edges is small enough. For the proof, we construct a non-Markovian coupling using a multiscale analysis of the environment. This is based on joint work with Andrea Lelli.

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