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 Electronic Communications in Probability > Vol. 5 (2000) > Paper 7 open journal systems 


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.


Full text: PDF

Pages: 67-71

Published on: April 24, 2000
Bibliography
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Electronic Communications in Probability. ISSN: 1083-589X