English

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 nn steps of the walk. A similar conclusion is drawn for the resistance metric.

Keywords

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