English

Volume and heat kernel fluctuations for the three-dimensional uniform spanning tree

Probability 2022-11-29 v1

Abstract

Let U\mathcal{U} be the uniform spanning tree on Z3\mathbb{Z}^{3}. We show the occurrence of log-logarithmic fluctuations around the leading order for the volume of intrinsic balls in U\mathcal{U}. As an application, we obtain similar fluctuations for the quenched heat kernel of the simple random walk on U\mathcal{U}.

Cite

@article{arxiv.2211.15031,
  title  = {Volume and heat kernel fluctuations for the three-dimensional uniform spanning tree},
  author = {Daisuke Shiraishi and Satomi Watanabe},
  journal= {arXiv preprint arXiv:2211.15031},
  year   = {2022}
}

Comments

39 pages, 20 figures

R2 v1 2026-06-28T07:14:20.452Z