Justification of the nonlinear Boltzmann equation for large times

We present a new approach to give a rigorous justification of the nonlinear Boltzmann equation as a scaling limit of discrete deterministic evolution for large times which avoids the convergence problems of the BBGKY hierarchy. The method is based on a careful analysis of the distribution of collision trees which are extracted from the dynamics. At the moment the proof is complete in the case of kinetic annihilation, in the case of collisional dynamics some estimates are still missing. New sharp conditions on the regularity of the velocity distribution have been discovered, and examples for the failure of the Boltzmann equation will be given.