Transient random walks in random environment on a Galton-Watson tree

E.F. Aidékon

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    20 Citations (Scopus)
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    Abstract

    We consider a transient random walk (X n ) in random environment on a Galton–Watson tree. Under fairly general assumptions, we give a sharp and explicit criterion for the asymptotic speed to be positive. As a consequence, situations with zero speed are revealed to occur. In such cases, we prove that X n is of order of magnitude n ¿, with . We also show that the linearly edge reinforced random walk on a regular tree always has a positive asymptotic speed, which improves a recent result of Collevecchio (Probab Theory Related 136(1):81–101, 2006).
    Original languageEnglish
    Pages (from-to)525-559
    JournalProbability Theory and Related Fields
    Volume142
    Issue number3-4
    DOIs
    Publication statusPublished - 2008

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