For p below the critical percolation probability and sufficiently small λ, the mixing time of nearest-neighbor Glauber dynamics on dynamical percolation is Θ(log N / λ) on the d-dimensional torus.
Information percolation and cutoff for the stochastic Ising model.Journal of the American Mathematical Society, 29(3):729–774, Sep 2015
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Mixing times of spin systems on dynamical percolation
For p below the critical percolation probability and sufficiently small λ, the mixing time of nearest-neighbor Glauber dynamics on dynamical percolation is Θ(log N / λ) on the d-dimensional torus.