  We consider a random model of diffusion and coagulation. A large number of
small particles are randomly scattered at an initial time. Each particle has
some integer mass and moves in a Brownian motion whose diffusion rate is
determined by that mass. When any two particles are close, they are liable to
combine into a single particle that bears the mass of each of them. Choosing
the initial density of particles so that, if their size is very small, a
typical one is liable to interact with a unit order of other particles in a
unit of time, we determine the macroscopic evolution of the system, in any
dimension d \geq 3. The density of particles evolves according to the
Smoluchowski system of PDEs, indexed by the mass parameter, in which the
interaction term is a sum of products of densities. Central to the proof is
establishing the so-called Stosszahlensatz, which asserts that, at any given
time, the presence of particles of two distinct masses at any given point in
macroscopic space is asymptotically independent, as the size of the particles
is taken towards zero.
