English

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

R2 v1 2026-07-22T17:19:21.326Z