Derivation of mean-field equations for stochastic particle systems

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 l...

Full description

Saved in:
Bibliographic Details
Published in:arXiv.org 2018-03
Main Authors: Jatuviriyapornchai, Watthanan, Grosskinsky, Stefan
Format: Article
Language:English
Subjects:
Conservation
Gelation
System effectiveness
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1703.08811