# Alternating Kinetics of Annihilating Random Walks Near a Free Interface

Source: [Alternating Kinetics of Annihilating Random Walks Near a Free Interface](<https://www.sota2.com/research/paper/68fa24692c2a3760193a3b90>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T09:09:53.973Z

Authors: L. Frachebourg, P. L. Krapivsky, S. Redner(2) \_\_INSTITUTION\_3\_\_ ENS, Paris, (2) Boston University)

Published: 1997-10-23T16:11:13.000Z

## 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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/cond-mat/9710252>)

[PDF](<https://arxiv.org/pdf/cond-mat/9710252.pdf>)