Generalized range of slow random walks on trees
| Autor: | Andreoletti, Pierre, Kagan, Alexis |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Ann. Inst. H. Poincar\'e Probab. Statist. 60(2): 1458-1509 (May 2024) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1214/23-AIHP1367 |
| Popis: | In this work, we are interested in the set of visited vertices of a tree $\mathbb{T}$ by a randomly biased random walk $\mathbb{X}:=(X_n,n \in \mathbb{N})$. The aim is to study a generalized range, that is to say the volume of the trace of $\mathbb{X}$ with both constraints on the trajectories of $\mathbb{X}$ and on the trajectories of the underlying branching random potential $\mathbb{V}:=(V(x), x \in \mathbb{T})$. 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 $\mathbb{X}$ and the ones of $\mathbb{V}$. Comment: 58 pages |
| Databáze: | arXiv |
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