Modul:   MAT675  PDE and Mathematical Physics

Mean-field Gibbs measures: Sharp and optimal rates of convergence

Vortrag von Dr. Rishabh Gvalani

Datum: 29.02.24  Zeit: 16.15 - 18.00  Raum: Y27H46

We study the invariant Gibbs measure of mean-field interacting diffusions and prove optimal global and local rates of convergence to its thermodynamic limit in the full sub-critical regime of temperatures \(T>T_c\) for a large class of potentials. Our proof relies on a non-asymptotic Sanov-type upper bound for the global rate (which is of independent interest itself) combined with an application of Stein's method for the local rate. We also apply these techniques to prove sharp exponential concentration inequalities for i.i.d empirical measures in negative Sobolev norms. This is joint work with Matías G. Delgadino (U. T. Austin).