Propagation of chaos for a balls into bins model
Consider a finite number of balls initially placed in L bins. At each time step a ball is taken from each non-empty bin. Then all the balls are uniformly reassigned into bins. This finite Markov chain is called Repeated Balls-into-Bins process and is a discrete time interacting particle system with parallel updating. We prove that, starting from a suitable (chaotic) set of initial states, as L → +∞, the numbers of balls in each bin become independent from the rest of the system i.e. we have propagation of chaos.