Scaling limits of Smoluchowski particles

Abstract

We prove a law of large numbers and a functional central limit theorem for the empirical density of a Marcus-Lushnikov model. The limiting density turns out to be the solution of a Smoluchowski equation, and the fluctuations around this limit are shown to be described by an Ornstein-Uhlenbeck process with drift term given by the linearization of the Smoluchowski operator.