A Stochastic Model for Coagulation-Fragmentation and Smoluchowski Equation
We consider a natural model for the coagulation-fragmentation process. In this model we have N Brownian particles that are travelling in the d–dimensional Euclidean space with a diffusion coefficient that is a function of the size of the particle. We regard the location of each particle as the center of a cluster and when two particles are sufficiently close, they coagulate to a larger cluster. Also clusters randomly fragment to smaller clusters. In a joint work with Alan Hammond, We show that if the range of the interaction is scaled like N 1 2−d , and as the number of particles N goes to infinity, the microscopic particle densities converge to solutions of the Smoluchoski’s equation.