An exponential formula for solving Boltzmann's equation for a Maxwellian gas

H. P. McKean

Research output: Contribution to journalArticle


A class of nonlinear Boltzmann-like equations are interpreted from a probabilistic point of view. The model leads to an exponential formula for the solution, which, in the special cases considered, can be made explicit by algebraic and combinatorial considerations involving derivations of an associated algebra and exponentials of these and a (commutative but possibly nonassociative) multipliaction (convolution) on a dual of this algebra. Kac's idea of "propagation of chaos" plays a central role in all this.

Original languageEnglish (US)
Pages (from-to)358-382
Number of pages25
JournalJournal of Combinatorial Theory
Issue number3
StatePublished - May 1967


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