Formal solution of a class of reaction-diffusion models: reduction to a single-particle problem.

We consider the trapping reaction A+B-->B in space dimension d<or=2. By formally eliminating the B particles from the problem, we derive an effective dynamics for the A particles from which the survival probability of a given A particle and the statistics of its spatial fluctuations can be calculated in a rather general way. The method can be extended to the study of annihilation and coalescence reactions, B+B-->0 or B, in d=2.