The H\"older continuity of the scaling limit of three-dimensional loop-erased random walk

Xinyi Li; Daisuke Shiraishi

The H\"older continuity of the scaling limit of three-dimensional loop-erased random walk

Probability 2022-10-27 v2

Authors: Xinyi Li , Daisuke Shiraishi

Abstract

Let $\beta$ be the growth exponent of the loop-erased random walk (LERW) in three dimensions. We prove that the scaling limit of 3D LERW is $h$ -H\"older continuous almost surely for all $h < 1/\beta$ , while not $1/\beta$ -H\"older continuous almost surely.

Keywords

loop-erased random walk scaling limit holder continuity growth exponent three dimensions

Cite

@article{arxiv.2111.04977,
  title  = {The H\"older continuity of the scaling limit of three-dimensional loop-erased random walk},
  author = {Xinyi Li and Daisuke Shiraishi},
  journal= {arXiv preprint arXiv:2111.04977},
  year   = {2022}
}

Comments

37 pages, 7 figures

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