Generalized range of slow random walks on trees
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2021
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| _version_ | 1866912034201796608 |
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| author | Andreoletti, Pierre Kagan, Alexis |
| author_facet | Andreoletti, Pierre Kagan, Alexis |
| contents | 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 $\mathbb{V}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05029 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Generalized range of slow random walks on trees Andreoletti, Pierre Kagan, Alexis Probability 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 $\mathbb{V}$. |
| title | Generalized range of slow random walks on trees |
| topic | Probability |
| url | https://arxiv.org/abs/2111.05029 |