Coagulation and branching process models of gravitational clustering

Smoluchowski's coagulation equation describes the growth of clustering in a system in which clusters coalesce irreversibly by binary mergers. If the rate with which two objects merge is proportional to the sum of their masses, and the process starts with all clusters having the same mass initially (monodisperse initial conditions), then the growth of clustering in the system can be derived from a Poisson Galton--Watson branching process. The branching process is consistent with, and provides a more detailed description of gravitational clustering from Poisson initial conditions, than the excursion set, Press--Schechter approach. The correspondence between the branching process and additive coagulation schemes is used to efficiently simulate realizations of the merger history tree. These results are easily extended to describe clustering from white noise Gaussian initial conditions. Extending this approach to describe clustering from Gaussian fields with arbitrary power spectra is more ...