## Abstract

Benjamini, Haggstrom, Peres and Steif introduced the model of dynamical random walk on Z^{d} [2]. This is a continuum of random walks indexed by a parameter t. They proved that for d = 3,4 there almost surely exist t such that the random walk at time t visits the origin infinitely often, but for d . 5 there almost surely do not exist such t. Hoffman showed that for d ≥ 2 there almost surely exists t such that the random walk at time t visits the origin only finitely many times [5]. We refine the results of [5] for dynamical random walk on Z^{2}, showing that with probability one the are times when the origin is visited only a finite number of times while other points are visited infinitely often.

Original language | English |
---|---|

Pages (from-to) | 1927-1951 |

Number of pages | 25 |

Journal | Electronic Journal of Probability |

Volume | 13 |

DOIs | |

State | Published - 1 Jan 2008 |

Externally published | Yes |

## Keywords

- Dynamical Random Walks
- Dynamical Sensitivity
- Random Walks

## Fingerprint

Dive into the research topics of 'A special set of exceptional times for dynamical random walk on Z^{2}'. Together they form a unique fingerprint.