Minkowski content of Brownian cut points

Abstract

Let $W(t)$, $0\le t\le T$, be a Brownian motion in ${\mathbb{R}}^d$, $d=2,3$. We say that $x$ is a cut point for $W$ if $x=W(t)$ for some $t\in (0,T)$ such that $W[0,t)$ and $W(t,T]$ are disjoint. In this work, we prove that a.s. the Minkowski content of the set of cut points for $W$ exists and is finite and non-trivial.

45 pages, 4 figures. Major revision according to the referee report. Accepted version. To appear at AIHP

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