Some generalizations of the trapping problem

We consider two effects on kinetics that have not generally been taken into account in analyses of classical trapping models for the reactions A + T → T and A + T → 0: the effects due to correlations in the initial positions of the Aʹs and those due to the state of mobility of each of the species. Our analysis is formulated in terms of three-dimensional Brownian motion. We give a heuristic treatment of the short-time regime based on statistical properties of the Wiener sausage. The effects of initially correlated positions are modelled in terms of a set of a multiplicity of A particles located at the origin.