Collision properties of the four-dimensional random walk trace

David A. Croydon; Daisuke Shiraishi; Satomi Watanabe

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arXiv · 2605.30755

Collision properties of the four-dimensional random walk trace

David A. Croydon·Daisuke Shiraishi·Satomi Watanabe

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Abstract

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 apply a result of Noda to derive a scaling limit for the collision time process. For three independent walks (in discrete time), we demonstrate infinitely many triple collisions occur.

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David A. Croydon, Daisuke Shiraishi, Satomi Watanabe. 2026-05-29. Collision properties of the four-dimensional random walk trace. https://arxiv.org/abs/2605.30755

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