Scaling limit of the occupation measure of random walk cut points

Yifan Gao; Xinyi Li; Petr Panov; Daisuke Shiraishi

Scaling limit of the occupation measure of random walk cut points

Probability 2023-10-17 v1

Authors: Yifan Gao , Xinyi Li , Petr Panov , Daisuke Shiraishi

Abstract

We consider the occupation measure of the cut points of a simple random walk on a $d$ -dimensional cubic lattice for $d = 2, 3$ , and we show that the scaling limit of the occupation measure in weak topology is the natural fractal measure on the Brownian cut points defined via its Minkowski content.

Keywords

random walk cut points occupation measure scaling limit weak topology minkowski content brownian cut points

Cite

@article{arxiv.2310.09592,
  title  = {Scaling limit of the occupation measure of random walk cut points},
  author = {Yifan Gao and Xinyi Li and Petr Panov and Daisuke Shiraishi},
  journal= {arXiv preprint arXiv:2310.09592},
  year   = {2023}
}

Comments

57 pages, 12 figures

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