The propagation of chaos for interacting individuals in a large population

Abstract This paper studies the approximation of interacting individuals' behaviors in a large population. We show “propagation of chaos”—that if individual initial behaviors are approximately independent and identically distributed, then their behaviors are also approximately independent on finite time spans and described by a common stochastic process. The initial approximate independence always propagates as long as deterministic approximation holds for their aggregate behavior. Our results not only formally represent our feeling of independence under anonymous interactions, they also allow us to apply the deterministic approximation process of aggregate behavior to obtain approximate distributions of individuals' behaviors.