Brownian earthworm

Krzysztof Burdzy; Zhen-Qing Chen; Soumik Pal

doi:10.1214/12-AOP831

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Home > Journals > Ann. Probab. > Volume 41 > Issue 6 > Article

November 2013 Brownian earthworm

Krzysztof Burdzy, Zhen-Qing Chen, Soumik Pal

Ann. Probab. 41(6): 4002-4049 (November 2013). DOI: 10.1214/12-AOP831

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Abstract

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.