  Diffusion limited reactions are studied in detail on the classical coalescing
process. We demonstrate how, with the aid of a recent renormalization group
approach, fluctuations can be integrated systematically. We thereby obtain an
exact relation between the microscopic physics (lattice structure, particle
shape and size) and the macroscopic decay rate in the law of mass action.
Moreover, we find a strong violation of the law of mass action. The
corresponding term in the kinetic equations originates in long wavelength
fluctuations and is a universal function of the macroscopic decay rate.
