  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.
