The Annals of Probability

Cone points of Brownian motion in arbitrary dimension

Yotam Alexander and Ronen Eldan

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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.

Article information

Ann. Probab., Volume 47, Number 5 (2019), 3143-3169.

Received: May 2018
Revised: December 2018
First available in Project Euclid: 22 October 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65] 52A22: Random convex sets and integral geometry [See also 53C65, 60D05]

Brownian motion cone points convex hull


Alexander, Yotam; Eldan, Ronen. Cone points of Brownian motion in arbitrary dimension. Ann. Probab. 47 (2019), no. 5, 3143--3169. doi:10.1214/19-AOP1335.

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