A capture problem in Brownian motion and eigenvalues of spherical domains

• Autores: Jesse Ratzkin, Andrejs Treibergs
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 361, Nº 1, 2009, págs. 391-405
• Idioma: inglés
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• Resumen

  • 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.