论文信息 - A capture problem in Brownian motion and eigenvalues of spherical domains

A capture problem in Brownian motion and eigenvalues of spherical domains

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.

Andrejs Treibergs | Jesse Ratzkin

[1] I. Chavel. Eigenvalues in Riemannian geometry , 1984 .

[2] D. Griffeath,et al. Capture Problems For Coupled Random Walks , 1991 .

[3] R. A. Silverman,et al. Special functions and their applications , 1966 .

[4] Zur Symmetrisierung von Funktionen auf Sphären. , 1973 .

[5] W. Burnside. Theory of Functions of a Complex Variable , 1893, Nature.

[6] G. Pólya,et al. Isoperimetric inequalities in mathematical physics , 1951 .

[7] F. Stenger. Numerical Methods Based on Sinc and Analytic Functions , 1993 .

[8] R. DeBlassie,et al. Exit times from cones in ℝn of Brownian motion , 1987 .

[9] L. Rayleigh,et al. The theory of sound , 1894 .

[10] R. D. D. Blassie,et al. Remark on exit times from cones in $$\mathbb{R}^n $$ of Brownian motion , 1988 .

[11] Qi-Man Shao,et al. Capture time of Brownian pursuits , 2001 .

[12] E. Sperner. Zur Symmetrisierung von Funktionen auf Sphären , 1973 .

[13] R. A. Silverman,et al. Theory of Functions of a Complex Variable , 1968 .