I consider a particle (random walker) diffusing in the y direction, with a transverse drift velocity f(y) in the x-direction and an absorbing boundary at x=0. The survival probability of the particle decays as t^-q. For any odd function f(y), q = 1/4 exactly, a result conjectured by Redner and Krapivsky. For generic f(y), q is a nontrivial functional of f(y). Some new exact results will be presented for a certain class of functions f(y).

University of Manchester