Random walks on dynamical percolation: mixing times, mean squared displacement and hitting times

2013/08/28 by Peres, Yuval, Stauffer, Alexandre, Steif, Jeffrey E. · 2 citations
#60K35 #60K37 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1308.6193

Abstract

We study the behavior of random walk on dynamical percolation. In this model, the edges of a graph G are either open or closed and refresh their status at rate μ while at the same time a random walker moves on G at rate 1 but only along edges which are open. On the d-dimensional torus with side length n, we prove that in the subcritical regime, the mixing times for both the full system and the random walker are n²/μ up to constants. We also obtain results concerning mean squared displacement and hitting times. Finally, we show that the usual recurrence transience dichotomy for the lattice Z^d holds for this model as well.

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• The speed of biased random walks among dynamical random conductances
• Mixing times of spin systems on dynamical percolation

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