Local times in critical generations of a random walk in random environment on trees
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912980920172544 |
|---|---|
| author | Kagan, Alexis |
| author_facet | Kagan, Alexis |
| contents | We consider a null-recurrent randomly biased walk $\mathbb{X}$ on a Galton-Watson tree in the (sub)-diffusive regime and we prove that properly renormalized, the local time in a critical generation converges in law towards some function of a stable continuous-state branching process. We also provide an explicit equivalent of the probability that critical generations are reached by the random walk $\mathbb{X}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16955 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local times in critical generations of a random walk in random environment on trees Kagan, Alexis Probability We consider a null-recurrent randomly biased walk $\mathbb{X}$ on a Galton-Watson tree in the (sub)-diffusive regime and we prove that properly renormalized, the local time in a critical generation converges in law towards some function of a stable continuous-state branching process. We also provide an explicit equivalent of the probability that critical generations are reached by the random walk $\mathbb{X}$. |
| title | Local times in critical generations of a random walk in random environment on trees |
| topic | Probability |
| url | https://arxiv.org/abs/2408.16955 |