Can a lamb reach a haven before being eaten by diffusing lions?

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, 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 . For large but finite N, we determine the unusual asymptotic form whose leading behavior is SN(z) ~ N−z2, with z = x/L. Simulations of the capture process very slowly converge to this asymptotic prediction as N reaches 10500.

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