Seminar
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| Location: | SLMath: Eisenbud Auditorium, Online/Virtual |
Hierarchies, cumulant functions, and higher-order propagation of chaos for mean-field interacting diffusions
Mean-field interacting diffusion processes are ubiquitous: originally introduced by McKean in the 1960’s as a toy model of interacting particles, they have found application in biology, economics, and machine learning, where instead of particles they respectively describe animals, agents, or parameters. Although there is an extensive literature studying propagation of chaos for these systems, sharp rates were only derived relatively recently in the seminal work of Daniel Lacker.
Adapting Lacker’s argument, I will discuss how quantitative propagation of chaos can be reframed as a stability property of the associated BBGKY hierarchy of equations. This perspective naturally raises the question of whether one can obtain sharp higher-order corrections to propagation of chaos. Addressing this requires additional tools, in particular, hierarchies of equations for the cumulant functions of the system. Based on joint work with Keefer Rowan.
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