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Continuously-variable survival exponent for random walks with movable partial reflectors

Ronald Dickman·Daniel ben-Avraham
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Abstract

We study a one-dimensional lattice random walk with an absorbing boundary at the origin and a movable partial reflector. On encountering the reflector, at site x, the walker is reflected (with probability r) to x-1 and the reflector is simultaneously pushed to x+1. Iteration of the transition matrix, and asymptotic analysis of the probability generating function show that the critical exponent delta governing the survival probability varies continuously between 1/2 and 1 as r varies between 0 and 1. Our study suggests a mechanism for nonuniversal kinetic critical behavior, observed in models with an infinite number of absorbing configurations.

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Ronald Dickman, Daniel ben-Avraham. 2001-04-24. Continuously-variable survival exponent for random walks with movable partial reflectors. https://doi.org/10.1103/physreve.64.020102

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