Capture of particles undergoing discrete random walks.

It is shown that particles undergoing discrete-time jumps in three dimensions, starting at a distance r0 from the center of an adsorbing sphere of radius R, are captured with probability (R-cσ)/r0 for r0>R, where c is related to the Fourier transform of the scaled jump distribution and σ 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 σ/(R<RADICAL><RADICAND>6</RADICAND></RADICAL>) depending only upon σ/R. These results have applications to computer simulations of reaction and aggregation. [ABSTRACT FROM AUTHOR]