Graph distance and effective resistance of the four-dimensional random walk trace
Probability
2026-02-20 v1
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 steps of the walk. A similar conclusion is drawn for the resistance metric.
Cite
@article{arxiv.2602.17076,
title = {Graph distance and effective resistance of the four-dimensional random walk trace},
author = {Daisuke Shiraishi and Satomi Watanabe},
journal= {arXiv preprint arXiv:2602.17076},
year = {2026}
}
Comments
30 pages, no figures