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

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

2001-04-24

arxiv.org/abs/cond-mat/0104470v1

Phys. Rev. E 64, 020102-1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 3 figures

Scientific paper

10.1103/PhysRevE.64.020102

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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