English

Drowsy Cheetah Hunting Antelopes: A Diffusing Predator Seeking Fleeing Prey

Statistical Mechanics 2009-11-10 v1

Abstract

We consider a system of three random walkers (a `cheetah' surrounded by two `antelopes') diffusing in one dimension. The cheetah and the antelopes diffuse, but the antelopes experience in addition a deterministic relative drift velocity, away from the cheetah, proportional to their distance from the cheetah, such that they tend to move away from the cheetah with increasing time. Using the backward Fokker-Planck equation we calculate, as a function of their initial separations, the probability that the cheetah has caught neither antelope after infinite time.

Keywords

Cite

@article{arxiv.cond-mat/0410449,
  title  = {Drowsy Cheetah Hunting Antelopes: A Diffusing Predator Seeking Fleeing Prey},
  author = {Karen Winkler and Alan J. Bray},
  journal= {arXiv preprint arXiv:cond-mat/0410449},
  year   = {2009}
}

Comments

5 pages

R2 v1 2026-07-22T11:09:14.579Z