# Heavy range of the randomly biased walk on Galton-Watson trees in the slow movement regime

1 PSPM - Probabilités, statistique, physique mathématique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : We consider the randomly biased random walk on trees in the slow movement regime as in [HS16], whose potential is given by a branching random walk in the boundary case. We study the heavy range up to the $n$-th return to the root, i.e., the number of edges visited more than $k_n$ times. For $k_n=n^\theta$ with $\theta\in(0,1)$, we obtain the convergence in probability of the rescaled heavy range, which improves one result of [AD20].
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Cited literature [21 references]

https://hal.archives-ouvertes.fr/hal-02945656
Contributor : Xinxin Chen <>
Submitted on : Tuesday, September 22, 2020 - 2:50:19 PM
Last modification on : Monday, October 5, 2020 - 10:11:47 AM

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• HAL Id : hal-02945656, version 1

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Xinxin Chen. Heavy range of the randomly biased walk on Galton-Watson trees in the slow movement regime. 2020. ⟨hal-02945656v1⟩

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