  Dynamical systems of N particles in \R^{D} interacting by a singular pair
potential of mean field type are considered. The systems are assumed to be of
gradient type and the existence of a macroscopic limit in the many particle
limit is established for a large class of singular interaction potentials in
the stochastic as well as the deterministic settings. The main assumption on
the potentials is an appropriate notion of quasi-convexity. When D=1 the
convergence result is sharp when applied to strongly singular repulsive
interactions and for a general dimension D the result applies to attractive
interactions with Lipschitz singular interaction potentials, leading to
stochastic particle solutions to the corresponding macroscopic aggregation
equations. The proof uses the theory of gradient flows in Wasserstein spaces of
Ambrosio-Gigli-Savaree.
