Georgia Institute of Technology College of Sciences

We investigate how fluctuations behave in large systems of interacting particles when the interaction is given by the Biot–Savart kernel, a key model from fluid dynamics. Our main result provides the first quantitative convergence rates for these fluctuations, and remarkably, the rates are optimal. The key idea is to compare the generators of the particle system and of the limiting fluctuation process in an infinite-dimensional setting. This comparison allows us to derive a sharp error bound for the fluctuations. Beyond the Biot–Savart case, the method is versatile and can also be applied to other singular interactions, such as the repulsive Coulomb kernel.