Speaker: Stefan Grosskinsky (University of Warwick)
Title: Mean-field dynamics for stochastic particle systems

Abstract:
The derivation of effective single-particle dynamics from interacting 
many-particle systems has a long history in the context of kinetic theory. 
While effective dynamics are often used as a starting point to study 
stochastic lattice gases in the theoretical physics literature, their 
rigorous derivation in this context has attracted attention only recently. 
We focus on the dynamics of cluster aggregation driven by monomer exchange, 
for which we derive effective rate equations in a mean-field scaling limit 
from an underlying particle system. 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 leads 
to non-uniqueness of stationary measures and a non-trivial ergodic behaviour, 
which can also involve metastable states and coarsening for condensing 
particle systems. This is joint work with Watthanan Jatuviriyapornchai and 
Andre Schlichting.