Propagation of Chaos in a Coagulation Model

TL;DR

This paper demonstrates that in a finite particle system with constant-rate coagulation, the macroscopic coagulation equation emerges in the thermodynamic limit, ensuring the propagation of chaos over time.

Contribution

It proves the global in time propagation of chaos for a coagulation model in the thermodynamic limit, connecting microscopic dynamics to the macroscopic coagulation equation.

Findings

Coagulation equation is recovered in the thermodynamic limit.

Propagation of chaos holds globally in time.

Finite particle system converges to the macroscopic model.

Abstract

A deterministic coalescing dynamics with constant rate for a particle system in a finite volume with a fixed initial number of particles is considered. It is shown that, in the thermodynamic limit, with the constraint of fixed density, the corresponding coagulation equation is recovered and global in time propagation of chaos holds.