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kollwit

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
Mathematik und Informatik

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 dependent selection. This is joint work with Tibor Mach and Jan Swart (Prague).



Angelegt am Freitag, 16.11.2018 09:27 von kollwit
Geändert am Freitag, 18.01.2019 12:43 von kollwit
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Stochastik
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