The Annals of Probability

Brownian earthworm

Krzysztof Burdzy, Zhen-Qing Chen, and Soumik Pal

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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.

Article information

Ann. Probab., Volume 41, Number 6 (2013), 4002-4049.

First available in Project Euclid: 20 November 2013

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Zentralblatt MATH identifier

Primary: 60J65: Brownian motion [See also 58J65]

Reflected Brownian motion


Burdzy, Krzysztof; Chen, Zhen-Qing; Pal, Soumik. Brownian earthworm. Ann. Probab. 41 (2013), no. 6, 4002--4049. doi:10.1214/12-AOP831.

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