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November 2013 Brownian earthworm
Krzysztof Burdzy, Zhen-Qing Chen, Soumik Pal
Ann. Probab. 41(6): 4002-4049 (November 2013). DOI: 10.1214/12-AOP831


We prove that the distance between two reflected Brownian motions, driven by the same white noise, outside a sphere in a $3$-dimensional flat torus does not converge to $0$, a.s., if the radius of the sphere is sufficiently small, relative to the size of the torus.


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Krzysztof Burdzy. Zhen-Qing Chen. Soumik Pal. "Brownian earthworm." Ann. Probab. 41 (6) 4002 - 4049, November 2013.


Published: November 2013
First available in Project Euclid: 20 November 2013

zbMATH: 1303.60074
MathSciNet: MR3161468
Digital Object Identifier: 10.1214/12-AOP831

Primary: 60J65

Keywords: reflected Brownian motion

Rights: Copyright © 2013 Institute of Mathematical Statistics

Vol.41 • No. 6 • November 2013
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