Graph distance and effective resistance of the four-dimensional random walk trace

Daisuke Shiraishi; Satomi Watanabe

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arXiv · 2602.17076

Graph distance and effective resistance of the four-dimensional random walk trace

Daisuke Shiraishi·Satomi Watanabe

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Abstract

Refining previous results, we establish a sharp asymptotic estimate on the expected graph distance between the origin and the terminal point of the trace of the first $n$ steps of the walk. A similar conclusion is drawn for the resistance metric.

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Daisuke Shiraishi, Satomi Watanabe. 2026-02-19. Graph distance and effective resistance of the four-dimensional random walk trace. https://arxiv.org/abs/2602.17076

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