Random walks on dynamical percolation: mixing times, mean squared displacement and hitting times
Journal article, 2015

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, we prove that in the subcritical regime, the mixing times for both the full system and the random walker are n^2/mu 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.

random walk


dynamical percolation

mixing times


Yuval Peres

Microsoft Research

Alexandre Stauffer

University of Bath

Jeffrey Steif

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Probability Theory and Related Fields

0178-8051 (ISSN) 1432-2064 (eISSN)

Vol. 162 3 487-530

Subject Categories



Basic sciences



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