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April 1998 Sets avoided by Brownian motion
Omer Adelman, Krzysztof Burdzy, Robin Pemantle
Ann. Probab. 26(2): 429-464 (April 1998). DOI: 10.1214/aop/1022855639

Abstract

A fixed two-dimensional projection of a three-dimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the two-dimensional projections with probability 1? Equivalently: three-dimensional Brownian motion hits any infinite cylinder with probability 1; does it hit all cylinders? This papers shows that the answer is no. Brownian motion in three dimensions avoids random cylinders and in fact avoids bodies of revolution that grow almost as fast as cones.

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Omer Adelman. Krzysztof Burdzy. Robin Pemantle. "Sets avoided by Brownian motion." Ann. Probab. 26 (2) 429 - 464, April 1998. https://doi.org/10.1214/aop/1022855639

Information

Published: April 1998
First available in Project Euclid: 23 September 2004

zbMATH: 0934.60016
MathSciNet: MR1626170
Digital Object Identifier: 10.1214/aop/1022855639

Subjects:
Primary: 60D05, 60J65

Rights: Copyright © 1998 Institute of Mathematical Statistics

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Vol.26 • No. 2 • April 1998
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