  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 $L\to+\infty$, the numbers of balls in each bin becomes
independent from the rest of the system i.e. we have propagation of chaos. We
furthermore study some equilibrium properties of the limiting nonlinear
process.
