### 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) |
---|---|

Pages (from-to) | 358-382 |

Number of pages | 25 |

Journal | Journal of Combinatorial Theory |

Volume | 2 |

Issue number | 3 |

State | Published - May 1967 |

### Fingerprint

### Cite this

*Journal of Combinatorial Theory*,

*2*(3), 358-382.

**An exponential formula for solving Boltzmann's equation for a Maxwellian gas.** / McKean, H. P.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory*, vol. 2, no. 3, pp. 358-382.

}

TY - JOUR

T1 - An exponential formula for solving Boltzmann's equation for a Maxwellian gas

AU - McKean, H. P.

PY - 1967/5

Y1 - 1967/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0002166759&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002166759&partnerID=8YFLogxK

M3 - Article

VL - 2

SP - 358

EP - 382

JO - Journal of Combinatorial Theory

JF - Journal of Combinatorial Theory

SN - 0021-9800

IS - 3

ER -