A duality method for mean-field limits with singular interactions

We introduce a new approach to derive mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to cover for the first time arbitrary square-integrable interaction forces at possibly vanishing temperature. The approach also provides convergence rates, and some statistical form of Central Limit Theorem at the limit.

This corresponds to joint works with D. Bresch, M. Duerinckx, and N. Khoury