  This paper develops a theory of propagation of chaos for a system of weakly
interacting particles whose terminal configuration is fixed as opposed to the
initial configuration as customary. Such systems are modeled by backward
stochastic differential equations. Under standard assumptions on the
coefficients of the equations, we prove propagation of chaos results and
quantitative estimates on the rate of convergence in Wasserstein distance of
the empirical measure of the interacting system to the law of a McKean-Vlasov
type equation. These results are accompanied by non-asymptotic concentration
inequalities. As an application, we derive rate of convergence results for
solutions of second order semilinear partial differential equations to the
solution of a partial differential written on an infinite dimensional space.
