Mean-field limit and propagation of chaos for topologically interacting particle systems
speaker: Stefano Rossi (Universität Zürich )abstract: I will consider systems of "topologically" interacting self-propelled agents: in this case, the interaction between two particles does not depend on the Euclidean distance between them but rather on the proximity rank. These topological models have proven to be very efficient in describing the dynamics of flocks of birds, locust swarms, fish schools, etc.
The focus will be on two topological mean-field models, a deterministic one of Cucker-Smale type and a stochastic jump process with topological transition probabilities, and on the validity of the statistical description of their evolution through effective partial differential equations.
In these cases the proofs of mean-field limit and propagation of chaos are made challenging precisely because of the topological character of the interaction, being in general discontinuous and depending on the positions of all the particles. In particular, the classic approaches using Dobrushin estimates and BBGKY hierarchies do not work without additional assumptions.
I will present different works in collaboration with D. Benedetto, E. Caglioti, P. Degond, T. Paul, and M. Pulvirenti where these results follow combining the use of other distances on the space of probability measures besides the classical Wasserstein one.
timetable:
Thu 25 Jan, 11:10 - 12:00, Aula Dini
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