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}.Comment: 13 pages, 6 figures, IOP format; v2: small changes in response to
referee and editor comment
