A Large Wiener Sausage from Crumbs

Omer Angel, Itaı Benjamini, Yuval Peres

Type: Article

Publication Date: 2000-01-01

Citations: 1

DOI: https://doi.org/10.1214/ecp.v5-1019

Abstract

Let $B(t)$ denote Brownian motion in $R^d$. It is a classical fact that for any Borel set $A$ in $R^d$, the volume $V_1(A)$ of the Wiener sausage $B[0,1]+A$ has nonzero expectation iff $A$ is nonpolar. We show that for any nonpolar $A$, the random variable $V_1(A)$ is unbounded.

Locations

Electronic Communications in Probability - View - PDF

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