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September 2019 Cone points of Brownian motion in arbitrary dimension
Yotam Alexander, Ronen Eldan
Ann. Probab. 47(5): 3143-3169 (September 2019). DOI: 10.1214/19-AOP1335

Abstract

We show that the convex hull of the path of Brownian motion in $n$-dimensions, up to time $1$, 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.

Citation

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Yotam Alexander. Ronen Eldan. "Cone points of Brownian motion in arbitrary dimension." Ann. Probab. 47 (5) 3143 - 3169, September 2019. https://doi.org/10.1214/19-AOP1335

Information

Received: 1 May 2018; Revised: 1 December 2018; Published: September 2019
First available in Project Euclid: 22 October 2019

zbMATH: 07145313
MathSciNet: MR4021247
Digital Object Identifier: 10.1214/19-AOP1335

Subjects:
Primary: 52A22, 60J65

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.47 • No. 5 • September 2019
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