A Large Wiener Sausage from Crumbs.

Omer Angel (Weizmann Institute of Science)
Itai Benjamini (Weizmann Institute of Science)
Yuval Peres (University of California, Berkeley)

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.

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Pages: 67-71

Publication Date: April 24, 2000

DOI: 10.1214/ECP.v5-1019

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