Genealogy in critical generations of a diffusive random walk in random environment on trees
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916456649719808 |
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| author | Kagan, Alexis |
| author_facet | Kagan, Alexis |
| contents | We consider the range $R^{(n)}$, the tree made up of visited vertices by a diffusive null-recurrent randomly biased walk $\mathbb{X}$ on a Galton-Watson tree $\mathbb{T}$ up to the $n$-th return time to its root and we consider the following genealogy problem: pick two vertices uniformly at random in a generation of order $n$ in the tree $R^{(n)}$. Where does the coalescence occur? it turns out that the coalescence happens either in the recent past or in the remote past. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08402 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Genealogy in critical generations of a diffusive random walk in random environment on trees Kagan, Alexis Probability We consider the range $R^{(n)}$, the tree made up of visited vertices by a diffusive null-recurrent randomly biased walk $\mathbb{X}$ on a Galton-Watson tree $\mathbb{T}$ up to the $n$-th return time to its root and we consider the following genealogy problem: pick two vertices uniformly at random in a generation of order $n$ in the tree $R^{(n)}$. Where does the coalescence occur? it turns out that the coalescence happens either in the recent past or in the remote past. |
| title | Genealogy in critical generations of a diffusive random walk in random environment on trees |
| topic | Probability |
| url | https://arxiv.org/abs/2410.08402 |