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A Capture Problem in Brownian Motion and Eigenvalues of Spherical Domains

Jesse Ratzkin·Andrejs Treibergs
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Abstract

We resolve a question of Bramson and Griffeath by showing that the expected capture time of four independent Brownian predators pursuing one Brownian prey on a line is finite. Our main tool is an eigenvalue estimate for a particular spherical domain, which we obtain by a coning construction and domain perturbation.

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Jesse Ratzkin, Andrejs Treibergs. 2005-05-12. A Capture Problem in Brownian Motion and Eigenvalues of Spherical Domains. https://arxiv.org/abs/math/0505274

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