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)
66 Downloads (Pure)

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 languageEnglish
Pages (from-to)487-530
Number of pages44
JournalProbability Theory and Related Fields
Volume162
Issue number3
Early online date9 Sep 2014
DOIs
Publication statusPublished - Aug 2015

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Hitting Time
Mixing Time
Random walk
Transience
Dichotomy
Recurrence
Torus
Closed
Graph in graph theory
Model
Graph

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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