Cone points of Brownian motion in arbitrary dimension
Probability
2018-05-08 v1 Metric Geometry
Abstract
We show that the convex hull of the path of Brownian motion in -dimensions, up to time , is a smooth set. As a consequence, we conclude that a Brownian motion in any dimension almost surely has no cone points for any cone whose dual cone is nontrivial.
Cite
@article{arxiv.1805.01958,
title = {Cone points of Brownian motion in arbitrary dimension},
author = {Yotam Alexander and Ronen Eldan},
journal= {arXiv preprint arXiv:1805.01958},
year = {2018}
}
Comments
Preliminary version