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Random walks on dynamical percolation Peres, Yuval


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 $\mu$, 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 $n$, when the bond parameter is subcritical, we determined (with A. Stauffer and J. Steif) the mixing times for both the full system and the random walker. The supercritical case is harder, but using evolving sets we were able (with J. Steif and P. Sousi) to analyze it for p sufficiently large. The critical and moderately supercritical cases remain open.

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