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

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-00652801
Contributor : Pierre Debs Connect in order to contact the contributor
Submitted on : Friday, December 16, 2011 - 11:56:13 AM
Last modification on : Tuesday, October 12, 2021 - 5:20:10 PM
Long-term archiving on: : Saturday, March 17, 2012 - 2:36:17 AM

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  • HAL Id : hal-00652801, version 1
  • ARXIV : 1112.3797

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Pierre Andreoletti, Pierre Debs. The number of generations entirely visited for recurrent random walks on random environment. Journal of Theoretical Probability, Springer, 2014, pp.518-538. ⟨hal-00652801⟩

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