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

Yuval Peres, Alexandre Stauffer, Jeffrey E. Steif

Research output: Contribution to journalArticle

9 Citations (Scopus)

### 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 $$\mu$$ 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 $${\mathbb {Z}}^d$$ holds for this model as well.
Original language English 487-530 44 Probability Theory and Related Fields 162 3 9 Sep 2014 https://doi.org/10.1007/s00440-014-0578-4 Published - Aug 2015

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Hitting Time
Mixing Time
Random walk
Transience
Dichotomy
Recurrence
Torus
Closed
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### Cite this

Random walks on dynamical percolation : mixing times, mean squared displacement and hitting times. / Peres, Yuval; Stauffer, Alexandre; Steif, Jeffrey E.

In: Probability Theory and Related Fields, Vol. 162, No. 3, 08.2015, p. 487-530.

Research output: Contribution to journalArticle

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