### Abstract

We study the first passage time properties of an integrated Brownian curve both in homogeneous and disordered environments. In a disordered medium we relate the scaling properties of this center-of-mass persistence of a random walker to the average persistence, the latter being the probability P̄_{pr}(t) that the expectation value 〈x(t)〉 of the walker's position after time t has not returned to the initial value. The average persistence is then connected to the statistics of extreme events of homogeneous random walks which can be computed exactly for moderate system sizes. As a result we obtain a logarithmic dependence P̄_{pr}(t) ∼ ln(t)-θ̄ with a new exponent θ̄ = 0.191 ± 0.002. We note a complete correspondence between the average persistence of random walks and the magnetization autocorrelation function of the transverse-field Ising chain, in the homogeneous and disordered case.

Original language | English |
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Pages (from-to) | 673-679 |

Number of pages | 7 |

Journal | Europhysics Letters |

Volume | 45 |

Issue number | 6 |

DOIs | |

Publication status | Published - Mar 15 1999 |

### ASJC Scopus subject areas

- Physics and Astronomy(all)

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## Cite this

*Europhysics Letters*,

*45*(6), 673-679. https://doi.org/10.1209/epl/i1999-00220-2