## Abstract

We consider simple random walk on the incipient infinite cluster for the spread-out model of oriented percolation on ℤ_{d} × ℤ_{+}. In dimensions d > 6, we obtain bounds on exit times, transition probabilities, and the range of the random walk, which establish that the spectral dimension of the incipient infinite cluster is frac {4}{3}, and thereby prove a version of the Alexander-Orbach conjecture in this setting. The proof divides into two parts. One part establishes general estimates for simple random walk on an arbitrary infinite random graph, given suitable bounds on volume and effective resistance for the random graph. A second part then provides these bounds on volume and effective resistance for the incipient infinite cluster in dimensions d > 6, by extending results about critical oriented percolation obtained previously via the lace expansion.

Original language | English |
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Pages (from-to) | 385-431 |

Number of pages | 47 |

Journal | Communications in Mathematical Physics |

Volume | 278 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2008 Mar |

Externally published | Yes |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics