A capture problem in Brownian motion and eigenvalues of spherical domains

Ratzkin, Jesse; Treibergs, Andrejs

doi:10.1090/S0002-9947-08-04505-4

A capture problem in Brownian motion and eigenvalues of spherical domains
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by Jesse Ratzkin and Andrejs Treibergs PDF

Trans. Amer. Math. Soc. 361 (2009), 391-405 Request permission

Abstract:

We resolve a question of Bramson and Griffeath by showing that the expected capture time of four predators pursuing a single prey, all moving by standard Brownian motion 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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