This was part of Machine Learning and Mean-Field Games

Propagation of chaos for maxima of particle systems with mean-field drift interaction

Martin Larsson, Carnegie-Mellon University
Tuesday, May 24, 2022

Abstract: We study the asymptotic behavior of normalized maxima of real-valued particles with mean-field drift interaction. Our main result establishes propagation of chaos: in the large population limit, the normalized maxima behave as those arising in an i.i.d. system where each particle follows the associated McKean-Vlasov limiting dynamics. Because the maximum depends on all particles, our result does not follow from classical propagation of chaos, where convergence to an i.i.d. limit holds for any fixed number of particles but not all particles simultaneously. This is joint work with Nikos Kolliopoulos and Zeyu Zhang.