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Alternating Kinetics of Annihilating Random Walks Near a Free Interface

L. Frachebourg·P. L. Krapivsky·S. Redner
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Abstract

The kinetics of annihilating random walks in one dimension, with the half-line x>0 initially filled, is investigated. The survival probability of the nth particle from the interface exhibits power-law decay, S_n(t)~t^{-alpha_n}, with alpha_n approximately equal to 0.225 for n=1 and all odd values of n; for all n even, a faster decay with alpha_n approximately equal to 0.865 is observed. From consideration of the eventual survival probability in a finite cluster of particles, the rigorous bound alpha_1<1/4 is derived, while a heuristic argument gives alpha_1 approximately equal to 3 sqrt{3}/8 = 0.2067.... Numerically, this latter value appears to be a stringent lower bound for alpha_1. The average position of the first particle moves to the right approximately as 1.7 t^{1/2}, with a relatively sharp and asymmetric probability distribution.

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L. Frachebourg, P. L. Krapivsky, S. Redner. 1997-10-23. Alternating Kinetics of Annihilating Random Walks Near a Free Interface. https://doi.org/10.1088/0305-4470%2F31%2F12%2F005

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