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Central limit theorem for Maxwellian molecules and truncation of the wild expansion
Author(s) -
Carlen E. A.,
Carvalho M. C.,
Gabetta E.
Publication year - 2000
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/(sici)1097-0312(200003)53:3<370::aid-cpa4>3.0.co;2-0
Subject(s) - boltzmann equation , truncation (statistics) , mathematics , limit (mathematics) , boltzmann constant , relaxation (psychology) , truncation error , computation , constructive , simple (philosophy) , upper and lower bounds , approximation error , mathematical analysis , statistical physics , mathematical physics , physics , quantum mechanics , statistics , psychology , social psychology , philosophy , process (computing) , algorithm , epistemology , computer science , operating system
We prove an L 1 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 n th 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.