A Capture Problem in Brownian Motion and Eigenvalues of Spherical Domains
Jesse Ratzkin, Andrejs Treibergs
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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