Kinetics of a diffusive capture process: Lamb besieged by a pride of lions

The survival probability, S-N(t), of a diffusing prey ('lamb') in the proximity of N diffusing predators (a 'pride of lions') in one dimension is investigated. When the lions are all to one side of the lamb, the survival probability decays as a non-universal power law, S-N(t) proportional to t(-beta N), with the decay exponent beta(N) proportional to ln N. The crossover behaviour as a function of the relative diffusivities of the lions and the lamb is also discussed. When N --> infinity, the lamb survival probability exhibits a log-normal decay, S-infinity(t) proportional to exp(- ln(2) t).