Smoluchowski's equation: rate of convergence of the Marcus-Lushnikov process

TL;DR

This paper establishes a quantitative rate at which the Marcus-Lushnikov process converges to the solution of Smoluchowski's coagulation equation, applicable to a broad class of kernels, using Wasserstein-type distances.

Contribution

It provides the first explicit convergence rate for the Marcus-Lushnikov process for kernels with homogeneity in (-∞,1], utilizing Wasserstein distances.

Findings

Convergence rate derived for a class of coagulation kernels.

Applicable to kernels with homogeneity degree in (-∞,1].

Uses Wasserstein-type distance effectively for coalescence phenomena.

Abstract

We derive a satisfying rate of convergence of the Marcus-Lushnikov process toward the solution to Smoluchowski's coagulation equation. Our result applies to a class of homogeneous-like coagulation kernels with homogeneity degree ranging in $(-\infty,1]$. It relies on the use of a Wasserstein-type distance, which has shown to be particularly well-adapted to coalescence phenomena.