## Abstract

The distribution of the first passage times (FPT) of a one-dimensional random walker to a target site follows a power law F(t)~t^{-}3 ^{/}2. We generalize this result to another situation pertinent to compact exploration and consider the FPT of a random walker with specific source and target points on an infinite fractal structure with spectral dimension d_{s}<2. We show that the probability density of the first return to the origin has the form F(t)~td_{s}^{/}2^{-}2, and the FPT to a specific target at distance r follows the law F(r,t)~rd _{w}^{-}d_{f}td_{s}^{/}2^{-}2, where d_{w} and d_{f} are the walk dimension and the fractal dimension of the structure, respectively. The distance dependence of F(r,t) reproduces the one of the mean FPT of a random walk in a confined domain.

Original language | English |
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Article number | 020104 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 83 |

Issue number | 2 |

DOIs | |

State | Published - 14 Feb 2011 |