Central limit theorem for Maxwellian molecules and truncation of the Wild expansion (2000)
| Venue: | Comm. Pure Appl. Math |
| Citations: | 12 - 5 self |
BibTeX
@ARTICLE{Carlen00centrallimit,
author = {E. A. Carlen and M. C. Carvalho and E. Gabetta},
title = {Central limit theorem for Maxwellian molecules and truncation of the Wild expansion},
journal = {Comm. Pure Appl. Math},
year = {2000},
volume = {53},
pages = {370--397}
}
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Abstract
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 been recently 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. 1.
