The heavy range of randomly biased walks on trees

Abstract : We focus on recurrent random walks in random environment (RWRE) on Galton-Watson trees. The range of these walks, that is the number of sites visited at some fixed time, has been studied in three different papers [AC18], [AdR17] and [dR16]. Here we study the heavy range: the number of edges visited at least α times for some integer α. The asymptotic behavior of this process when α is a power of the number of steps of the walk is given for all the recurrent cases. It turns out that this heavy range plays a crucial role in the rate of convergence of an estimator of the environment from a single trajectory of the RWRE.
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Contributor : Pierre Andreoletti <>
Submitted on : Wednesday, December 19, 2018 - 5:28:48 PM
Last modification on : Thursday, January 17, 2019 - 2:38:04 PM
Document(s) archivé(s) le : Thursday, March 21, 2019 - 2:17:52 AM


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  • HAL Id : hal-01849187, version 3
  • ARXIV : 1811.02226


Pierre Andreoletti, Roland Diel. The heavy range of randomly biased walks on trees. 2018. ⟨hal-01849187v3⟩



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