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

Yuval Peres; Alexandre Stauffer; Jeffrey E. Steif

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arXiv · 1308.6193

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

Yuval Peres·Alexandre Stauffer·Jeffrey E. Steif

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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 n^2/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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BibTeX RIS

Yuval Peres, Alexandre Stauffer, Jeffrey E. Steif. 2013-08-28. Random walks on dynamical percolation: mixing times, mean squared displacement and hitting times. https://arxiv.org/abs/1308.6193

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