  The Smoluchowski coagulation-diffusion PDE is a system of partial
differential equations modelling the evolution in time of mass-bearing Brownian
particles which are subject to short-range pairwise coagulation. This survey
presents a fairly detailed exposition of the kinetic limit derivation of the
Smoluchowski PDE from a microscopic model of many coagulating Brownian
particles that was undertaken in [11]. It presents heuristic explanations of
the form of the main theorem before discussing the proof, and presents key
estimates in that proof using a novel probabilistic technique. The survey's
principal aim is an exposition of this kinetic limit derivation, but it also
contains an overview of several topics which either motivate or are motivated
by this derivation.
