A Capture Problem in Brownian Motion and Eigenvalues of Spherical Domains
Probability
2016-02-02 v1 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.math/0505274,
title = {A Capture Problem in Brownian Motion and Eigenvalues of Spherical Domains},
author = {Jesse Ratzkin and Andrejs Treibergs},
journal= {arXiv preprint arXiv:math/0505274},
year = {2016}
}
Comments
11 pages, 3 figures