Recurrence and transience of multidimensional elephant random walks
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866910971637792768 |
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| author | Qin, Shuo |
| author_facet | Qin, Shuo |
| contents | We prove a conjecture by Bertoin that the multi-dimensional elephant random walk on $\mathbb{Z}^d$($d\geq 3$) is transient and the expected number of zeros is finite. We also provide some estimates on the rate of escape. In dimensions $d= 1, 2$, we prove that phase transitions between recurrence and transience occur at $p=(2d+1)/(4d)$.
Let $S$ be an elephant random walk with parameter $p$. For $p \leq 3/4$, we provide a Berry-Esseen type bound for properly normalized $S_n$. For $p>3/4$, the distribution of $\lim_{n\to \infty} S_n/n^{2p-1}$ will be studied. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_09795 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Recurrence and transience of multidimensional elephant random walks Qin, Shuo Probability We prove a conjecture by Bertoin that the multi-dimensional elephant random walk on $\mathbb{Z}^d$($d\geq 3$) is transient and the expected number of zeros is finite. We also provide some estimates on the rate of escape. In dimensions $d= 1, 2$, we prove that phase transitions between recurrence and transience occur at $p=(2d+1)/(4d)$. Let $S$ be an elephant random walk with parameter $p$. For $p \leq 3/4$, we provide a Berry-Esseen type bound for properly normalized $S_n$. For $p>3/4$, the distribution of $\lim_{n\to \infty} S_n/n^{2p-1}$ will be studied. |
| title | Recurrence and transience of multidimensional elephant random walks |
| topic | Probability |
| url | https://arxiv.org/abs/2309.09795 |