Planar Brownian motion winds evenly along its trajectory
Probability
2021-02-25 v1
Abstract
Let be the set of points around which a planar Brownian motion winds at least times. We prove that the random measure on the plane with density with respect to the Lebesgue measure converges almost surely weakly, as tends to infinity, towards the occupation measure of the Brownian motion.
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}
}