### 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 |
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Pages (from-to) | 487-530 |

Number of pages | 44 |

Journal | Probability Theory and Related Fields |

Volume | 162 |

Issue number | 3 |

Early online date | 9 Sep 2014 |

DOIs | |

Publication status | Published - Aug 2015 |

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## Cite this

Peres, Y., Stauffer, A., & Steif, J. E. (2015). Random walks on dynamical percolation: mixing times, mean squared displacement and hitting times.

*Probability Theory and Related Fields*,*162*(3), 487-530. https://doi.org/10.1007/s00440-014-0578-4