  We study a class of one-dimensional particle systems with true (Bird type)
binary interactions, which includes Kac's model of the Boltzmann equation and
nonlinear equations for the evolution of wealth distribution arising in kinetic
economic models. We obtain explicit rates of convergence for the Wasserstein
distance between the law of the particles and their limiting law, which are
linear in time and depend in a mild polynomial manner on the number of
particles. The proof is based on a novel coupling between the particle system
and a suitable system of nonindependent nonlinear processes, as well as on
recent sharp estimates for empirical measures.

Probability