Anja Sturm, Göttingen: Recursive tree processes and mean-field limits of interacting particle systems (Oberseminar Mathematische Stochastik)
Mittwoch, 23.01.2019 17:00 im Raum SRZ 205
In this talk we consider interacting particle systems, their description via
graphical respresentations (stochastic flows) and their dual processes.
We then focus on systems where the underlying lattice is given by the complete graph
and consider the mean-field limit for which the number of vertices tends to infinity.
We are not only interested in the mean-field limit of a single process, but
mainly in how several coupled processes behave in the limit. These turn out to
be closely related (dual in some sense) to recursive tree processes (RTP), which are
generalizations of Markov chains with a tree-like time parameter, that were studied
by Aldous and Bandyopadyay in discrete time (alongside corresponding recursive
distributional equations (RTP)).
We illustrate our theory with a particle system with cooperative branching and also
point out connections to recent work by Baake, Cordero and Hummel using RTPs
to describe the ancestral selection graph in a model with mutation and frequency
This is joint work with Tibor Mach and Jan Swart (Prague).