A Capture Problem in Brownian Motion and Eigenvalues of Spherical Domains

Details A Capture Problem in Brownian Motion and Eigenvalues of Spherical Domains A Capture Problem in Brownian Motion and Eigenvalues of Spherical Domains

2005-05-12

arxiv.org/abs/math/0505274v1

Mathematics

Probability

11 pages, 3 figures

Scientific paper

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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