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Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions

P. L. Krapivsky·S. Redner
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Abstract

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) is proportional to t^{-beta_N}, with the decay exponent beta_N proportional to ln N. The crossover behavior as a function of the relative diffusivities of the lions and the lamb is also discussed. When N--->oo, the lamb survival probability exhibits a log-normal decay, exp(-ln^2 t).

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P. L. Krapivsky, S. Redner. 1996-03-28. Kinetics of a Diffusive Capture Process: Lamb Besieged by a Pride of Lions. https://doi.org/10.1088/0305-4470%2F29%2F17%2F011

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