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Generalized range of slow random walks on trees

Abstract : In this work we are interested in the set of visited vertices of a tree T by a randomly biased random walk X := (Xn, n ∈ N). The aim is to study a generalized range, that is to say the volume of the trace of X with both constraints on the trajectories of X and on the trajectories of the underlying branching random potential V := (V (x), x ∈ T). Focusing on slow regime's random walks (see [HS16b], [AC18]) we prove a general result and detail examples. These examples exhibit many different behaviors for a wide variety of ranges, showing the interactions between trajectories of X and the ones of V.
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https://hal.archives-ouvertes.fr/hal-03420519
Contributor : Alexis Kagan Connect in order to contact the contributor
Submitted on : Friday, November 19, 2021 - 11:49:12 AM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM

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  • HAL Id : hal-03420519, version 2

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Pierre Andreoletti, Alexis Kagan. Generalized range of slow random walks on trees. 2021. ⟨hal-03420519v2⟩

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