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 $x+1.\mathrm{}$ 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.

• Received 24 April 2001

DOI:https://doi.org/10.1103/PhysRevE.64.020102