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Pré-Publication, Document De Travail Année : 2007

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

Résumé

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 $n^{\Lambda}$, with $\Lambda \in (0,1)$. 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~\cite{Col06}.
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Dates et versions

hal-00180001 , version 1 (17-10-2007)

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Elie Aidekon. transient random walks in random environment on a Galton-Watson tree. 2007. ⟨hal-00180001⟩
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