Description
Interacting particle systems can often be constructed from a graphical
representation, by applying local maps at the times of associated Poisson
processes. This leads to a natural coupling of systems started in different
initial states. In the talk, we will look at interacting particle systems on
the complete graph in the mean-field limit, i.e., as the number of vertices
tends to infinity. We will not only be interested in the mean-field limit of a
single process, but mainly in how several coupled processes behave in the
limit. In particular, we want to know how sensitive the Poisson construction
is to small changes in the initial state. This turns out to be closely related
to recursive tree processes as studied by Aldous and Bandyopadyay, which are a
sort of Markov chains in which time has a tree-like structure and in which the
state of each vertex is a random function of its descendants. The abstract
theory will be demonstrated on an example of a particle system with
cooperative branching and deaths.
This is joint work with Anja Sturm and Tibor Mach.