English

Convergence in natural parametrization of random walk frontier

Probability 2025-04-21 v1

Abstract

In this paper, we show that the frontier of planar random walk converges weakly under natural parametrization to that of planar Brownian motion. As an intermediate result, we also show the convergence of the renormalized occupation measure.

Keywords

Cite

@article{arxiv.2504.13743,
  title  = {Convergence in natural parametrization of random walk frontier},
  author = {Yifan Gao and Xinyi Li and Runsheng Liu and Xiangyi Liu and Daisuke Shiraishi},
  journal= {arXiv preprint arXiv:2504.13743},
  year   = {2025}
}

Comments

33 pages, 4 figures