The kinetic limit of a system of coagulating planar Brownian particles

We study a model of mass-bearing coagulating planar Brownian particles. Coagulation is prone to occur when two particles become within a distance of order $ϵ$. We assume that the initial number of particles is of the order of $| \log \epsilon |. Under suitable assumptions on the initial distribution of particles and the microscopic coagulation propensities, we show that the macroscopic particle densities satisfy a Smoluchowski-type equation.