The number of generations entirely visited for recurrent random walks on random environment

The number of generations entirely visited for recurrent random walks on random environment

In this paper we are interested in a random walk in a random environment on a super-critical Galton-Watson tree. We focus on the recurrent cases already studied by Y. Hu and Z. Shi and G. Faraud. We prove that the largest generation entirely visited by these walks behaves like log n and that the con...

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Bibliographic Details
Main Authors: Andreoletti, Pierre, Debs, Pierre
Format: Journal Article
Language:English
Published: 16-12-2011
Subjects:
Mathematics - Probability
Online Access:Get full text
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Summary:In this paper we are interested in a random walk in a random environment on a super-critical Galton-Watson tree. We focus on the recurrent cases already studied by Y. Hu and Z. Shi and G. Faraud. We prove that the largest generation entirely visited by these walks behaves like log n and that the constant of normalization which differs from a case to another is function of the inverse of the constant of Biggins' law of large number for branching random walks.
DOI:10.48550/arxiv.1112.3797