Central limit theorem for Maxwellian molecules and truncation of the Wild expansion

We prove an L-1 bound on the error made when the Wild summation for solutio ns of the Boltzmann equation for a gas of Maxwellian molecules is truncated at the n(th) stage. This gives quantitative control over the only construc tive method known for solving the Boltzmann equation. As such, it has recen tly been applied to numerical computation but without control on the approx imation made in truncation. We also show that our bound is qualitatively sh arp and that it leads to a simple proof of the exponentially fast rate of r elaxation to equilibrium for Maxwellian molecules along lines originally su ggested by McKean. (C) 2000 John Wiley & Sons, Inc.