Equilibrium Fluctuations for a Model of Coagulating-Fragmenting Planar Brownian Particles

We study a model of mass-bearing coagulating-fragmenting planar Brownian particles. Coagulation occurs when two particles are within a distance of order epsilon. Our model is macroscopically described by an inhomogeneous Smoluchowski's equation in the low epsilon limit provided that the initial number of particles N is of order |log epsilon|. When a detailed balance condition is satisfied, we establish a central limit theorem by showing that in the low epsilon limit, the particle density fluctuation fields obey an Ornstein-Uhlenbeck stochastic differential equation.