Can a Lamb Reach a Haven Before Being Eaten by Diffusing Lions?
Abstract
We study the survival of a single diffusing lamb on the positive half line in the presence of N diffusing lions that all start at the same position L to the right of the lamb and a haven at x=0. If the lamb reaches this haven before meeting any lion, the lamb survives. We investigate the survival probability of the lamb, S_N(x,L), as a function of N and the respective initial positions of the lamb and the lions, x and L. We determine S_N(x,L) analytically for the special cases of N=1 and N--->oo. For large but finite N, we determine the unusual asymptotic form whose leading behavior is S_N(z)\simN^{-z^2}, with z=x/L. Simulations of the capture process very slowly converge to this asymptotic prediction as N reaches 10^{500}.
Cite
@article{arxiv.1203.2985,
title = {Can a Lamb Reach a Haven Before Being Eaten by Diffusing Lions?},
author = {Alan Gabel and Satya N. Majumdar and Nagendra K. Panduranga and S. Redner},
journal= {arXiv preprint arXiv:1203.2985},
year = {2012}
}
Comments
13 pages, 6 figures, IOP format; v2: small changes in response to referee and editor comments