Capture of particles undergoing discrete random walks.

It is shown that particles undergoing discrete-time jumps in three dimensions, starting at a distance r(0) from the center of an adsorbing sphere of radius R, are captured with probability (R-c sigma)/r(0) for r(0)>>R, where c is related to the Fourier transform of the scaled jump distribution and sigma is the distribution's root-mean square jump length. For particles starting on the surface of the sphere, the asymptotic survival probability is nonzero (in contrast to the case of Brownian diffusion) and has a universal behavior sigma/(R square root(6)) depending only upon sigma/R. These results have applications to computer simulations of reaction and aggregation.