Trapping of Brownian particles by random spheres of different radii

We analyze the survival of a Brownian particle moving among randomly distributed spherical traps of two different radii. All of the results known in the case of identical traps, the mean-field Smoluchowski solution, the lowest order correction of this solution, the cumulant expansion, and the long-time behavior, are generalized to the case of two types of traps. Our approach is readily extended to deal with trapping spheres having more than two different radii.