Diffusions limited reactions in confined geometries exhibit all aspects of nonequilibrium dynamics, such as anomalous kinetics, self-organization and dynamical phase transitions, and have therefore been the subject of extensive research in recent years. In this paper we review the method of interparticle distribution functions (IPDF) which was originally introduced for deriving the exact kinetics of the diffusion-limited coalescence process, A+A→A, in one dimension. We explain the IPDF method and review variants of the coalescence model which can be solved exactly through this technique. We then consider strategies for approximations based on the IPDF method and review applications to coalescence with finite reaction rates (away from the strictly diffusion-controlled regime), many-body reactions (nA→mA), and the contact process. We conclude with a discussion of open, interesting problems and possible ways to their solution.
Diffusion-limited reactions of hard-core particles in one dimension