Can a lamb reach a haven before being eaten by diffusing lions?
نویسندگان
چکیده
We study the survival of a single diffusing lamb on the positive half line in the presence of N diffusing lions 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, SN (x,L), as a function of N and the respective initial positions of the lamb and the lions, x and L. We determine SN (x,L) analytically for the special cases of N = 1 and N → ∞. For large but finite N , we determine the unusual asymptotic form whose leading behavior is SN (z) ∼ N 2 , with z = x/L. Simulations of the capture process very slowly converge to this asymptotic prediction as N reaches 10. PACS numbers: 02.50.Cw, 05.40.-a, 05.50.+q Can a Lamb Reach a Haven Before Being Eaten by Diffusing Lions? 2
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