While random processes in static random structures are relatively well understood, their analysis in the dynamic setting is still in its infancy. Recently, progress has been made for reaction diffusion networks and for random walks in dynamic random environments. Sometimes, the dynamics alters the qualitative behavior, in other cases it does not. It is believed that local conservation laws in the dynamics play a crucial role, but very little is known to date.
The projects related to this theme are:
Optimisation of polling networks with limited service disciplines