Average persistence of random walks

H. Rieger, F. Iglói

Research output: Contribution to journalArticle

20 Citations (Scopus)

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 P̄pr(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 P̄pr(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 languageEnglish
Pages (from-to)673-679
Number of pages7
JournalEurophysics Letters
Volume45
Issue number6
DOIs
Publication statusPublished - Mar 15 1999

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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