Satomi Watanabe

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math.PR2026

Collision properties of the four-dimensional random walk trace

David A. Croydon, Daisuke Shiraishi, Satomi Watanabe

We consider collisions of multiple random walks on the trace of a simple random walk on the four-dimensional integer lattice. For two independent walks (in continuous time), we app…

math.PR2026

Largest-loop-first loop-erased random walk on $Z^{4}$

Daisuke Shiraishi, Satomi Watanabe

Let $S = (S (n))$ be a simple random walk on $Z^{d}$ started at the origin. We study a loop-erasing procedure of $S [0, n]$ that differs from Lawler's chronological loop-eras…

Collision properties of the four-dimensional random walk trace

Largest-loop-first loop-erased random walk on Z4

Largest-loop-first loop-erased random walk on $Z^{4}$