For nearest-neighbour spin systems on subcritical dynamical percolation, sufficiently slow edge dynamics force mixing time Θ(λ^{-1} log N), with cutoff as λ→0.
Random walk on dynamical per- colation in euclidean lattices: separating critical and supercritical regimes
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Step-reinforced random walks on finite groups converge exponentially to uniform; on cycles mixing time jumps from logarithmic to polynomial at alpha=1/2, while on hypercubes reinforcement slows mixing with cutoff at d log d over F(alpha)(1-alpha).
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Mixing times of spin systems on dynamical percolation
For nearest-neighbour spin systems on subcritical dynamical percolation, sufficiently slow edge dynamics force mixing time Θ(λ^{-1} log N), with cutoff as λ→0.
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Mixing times of step-reinforced random walks
Step-reinforced random walks on finite groups converge exponentially to uniform; on cycles mixing time jumps from logarithmic to polynomial at alpha=1/2, while on hypercubes reinforcement slows mixing with cutoff at d log d over F(alpha)(1-alpha).