We study the evolution of a system of n particles {(xi, vi)} n i=1 in IR . That system is a conservative system with a Hamiltonian of the form H[μ] = W 2 2 (μ, ν n), where W2 is the Wasserstein distance and μ is a discrete measure concentrated on the set {(xi, vi)} n i=1. Typically, μ(0) is a discrete measure approximating an initial L density and can be chosen randomly. When d = 1, our results...