### Abstract

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 language | English (US) |
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Pages (from-to) | 358-382 |

Number of pages | 25 |

Journal | Journal of Combinatorial Theory |

Volume | 2 |

Issue number | 3 |

DOIs | |

State | Published - May 1967 |

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## Cite this

McKean, H. P. (1967). An exponential formula for solving Boltzmann's equation for a Maxwellian gas.

*Journal of Combinatorial Theory*,*2*(3), 358-382. https://doi.org/10.1016/S0021-9800(67)80035-8