Author

Shuo Qin

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Preprint Sep 2026

Recurrence and range of the balanced excited random walk M(2,1,2)

We prove that the planar balanced excited random walk $M(2,1,2)$ is recurrent. This walk takes a horizontal simple random walk step on its first departure from each vertex and a planar simple random walk step on every later departure. Moreover, the number of distinct vertices visited before time $n$, multiplied by $(\l...

Shuo Qin · 0 citations

Preprint Sep 2026

Cover times and ranges of elephant random walks

We study cover times on discrete tori and ranges on $\mathbb{Z}^d$ for elephant random walks with memory parameter $p\in[0,1)$. In dimension one there is a phase transition at $p=3/4$. Away from criticality we determine the exact first-order asymptotics of the mean cover time, while at $p=3/4$ the mean is of order $L^2...

Shuo Qin · 2 citations · ⚡1