Title: Propagation of chaos and fluctuations for non-exchangeable diffusions

 

Abstract: We study a system of interacting diffusions with heterogeneous pairwise interactions, so the particle system is non-exchangeable. In the first part of the talk, we develop a quantitative, non-asymptotic approach to mean field approximation by comparing the law of any subcollection of particles with a suitably chosen product measure and proving sharp relative entropy bounds. The proof uses a BBGKY hierarchy adapted to the non-exchangeable setting and an unexpected connection with first-passage percolation.

 

In the second part, we establish a central limit theorem for fluctuations of the global empirical measure around the McKean-Vlasov limit. We show that, under explicit denseness conditions on the weighted graph encoding the interaction strengths, the limiting fluctuations coincide with those in the classical mean-field case. A crucial ingredient is the sharp propagation of chaos estimates developed in the first part.

 

Based on joint work with Daniel Lacker and Fuzhong Zhou, and on work in progress with Mykhaylo Shkolnikov.