Smoluchowski’s equation: Rate of convergence of the Marcus–Lushnikov process

We derive a satisfying rate of convergence of the Marcus–Lushnikov process towards the solution to Smoluchowski’s coagulation equation. Our result applies to a class of homogeneous-like coagulation kernels with homogeneity degree ranging in (−∞,1](−∞,1]. It relies on the use of a Wasserstein-type distance, which has shown to be particularly well-adapted to coalescence phenomena. It was introduced and used in preceding works (Fournier and Laurençot (2006) [7]) and (Fournier and Löcherbach (2009) [8]).