Recurrence and transience of multidimensional elephant random walks
Shuo Qin
Shuo Qin
Sep 2023
0被引用
0笔记
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摘要原文
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.
