English

Planar Brownian motion winds evenly along its trajectory

Probability 2021-02-25 v1

Abstract

Let DND_N be the set of points around which a planar Brownian motion winds at least NN times. We prove that the random measure on the plane with density 2πN1DN2 \pi N 1_{D_N} with respect to the Lebesgue measure converges almost surely weakly, as NN tends to infinity, towards the occupation measure of the Brownian motion.

Keywords

Cite

@article{arxiv.2102.12372,
  title  = {Planar Brownian motion winds evenly along its trajectory},
  author = {Isao Sauzedde},
  journal= {arXiv preprint arXiv:2102.12372},
  year   = {2021}
}
R2 v1 2026-06-23T23:28:42.674Z