# Derivation of mean-field equations for stochastic particle systems

## TL;DR

This paper derives mean-field equations for large stochastic particle systems on complete graphs, establishing chaos propagation and linking phenomena like gelation and condensation.

## Contribution

It provides a rigorous derivation of mean-field rate equations and analyzes the limit dynamics, connecting to recent growth models and phenomena.

## Key findings

- Propagation of chaos under growth conditions
- Limit dynamics as a non-linear birth-death process
- Conservation laws and non-uniqueness of stationary states

## Abstract

We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under generic growth conditions on particle jump rates, and the limit provides a master equation for the single site dynamics of the particle system, which is a non-linear birth death chain. Conservation of mass in the particle system leads to conservation of the first moment for the limit dynamics, and to non-uniqueness of stationary distributions. Our findings are consistent with recent results on exchange driven growth, and provide a connection between the well studied phenomena of gelation and condensation.