Pl. Krapivsky et S. Redner, KINETICS OF A DIFFUSIVE CAPTURE PROCESS - LAMB BESIEGED BY A PRIDE OFLIONS, Journal of physics. A, mathematical and general, 29(17), 1996, pp. 5347-5357
The survival probability, S-N(t), of a diffusing prey ('lamb') in the
proximity of N diffusing predators (a 'pride of lions') in one dimensi
on is investigated. When the lions are all to one side of the lamb, th
e survival probability decays as a non-universal power law, S-N(t) pro
portional to t(-beta N), with the decay exponent beta(N) proportional
to ln N. The crossover behaviour as a function of the relative diffusi
vities of the lions and the lamb is also discussed. When N --> infinit
y, the lamb survival probability exhibits a log-normal decay, S-infini
ty(t) proportional to exp(- ln(2) t).