Cone points of Brownian motion in arbitrary dimension

Yotam Alexander; Ronen Eldan

doi:https://doi.org/10.1214/19-AOP1335

Cone points of Brownian motion in arbitrary dimension

Yotam Alexander, Ronen Eldan

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	3143-3169
Number of pages	27
Journal	Annals of Probability
Volume	47
Issue number	5
DOIs	https://doi.org/10.1214/19-AOP1335
State	Published - Sep 2019

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title = "Cone points of Brownian motion in arbitrary dimension",

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.",

author = "Yotam Alexander and Ronen Eldan",

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year = "2019",

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AU - Alexander, Yotam

AU - Eldan, Ronen

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N2 - 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.

AB - 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.

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M3 - مقالة

SN - 0091-1798

VL - 47

SP - 3143

EP - 3169

JO - Annals of Probability

JF - Annals of Probability

IS - 5

ER -

Cone points of Brownian motion in arbitrary dimension

Abstract

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