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Preprints, Working Papers, ... Year : 2022

Generalized range of slow random walks on trees

Pierre Andreoletti
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Alexis Kagan
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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 the trajectories of X and the ones of V.
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Dates and versions

hal-03420519 , version 1 (09-11-2021)
hal-03420519 , version 2 (19-11-2021)
hal-03420519 , version 3 (06-11-2022)


  • HAL Id : hal-03420519 , version 3


Pierre Andreoletti, Alexis Kagan. Generalized range of slow random walks on trees. 2022. ⟨hal-03420519v3⟩
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