2 4 Ju n 20 09 Expansion of the propagation of chaos for Bird and Nanbu systems

The Bird and Nanbu systems are particle systems used to approximate the solution of the mollified Boltzmann equation. In particular, they have the propagation of chaos property. Following [GM94], we use coupling techniques and results on branching processes to write an expansion of the error in the propagation of chaos in terms of the number of particles, for slightly more general systems than the ones cited above. As explained in [DPR09a] and [DPR09b], this result will lead to the proof of the convergence of U -statistics for these systems.