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

Abstract

We prove an L1 bound on the error made when the Wild summation for solutions of the Boltzmann equation for a gas of Maxwellian molecules is truncated at the nth stage. This gives quantitative control over the only constructive method known for solving the Boltzmann equation. As such, it has recently been applied to numerical computation but without control on the approximation made in truncation. We also show that our bound is qualitatively sharp and that it leads to a simple proof of the exponentially fast rate of relaxation to equilibrium for Maxwellian molecules along lines originally suggested by McKean. © 2000 John Wiley & Sons, Inc.