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A geometric rate of convergence to the equilibrium for Boltzmann processes with multiple particle interactions

Published online by Cambridge University Press:  14 July 2016

Brigitte Chauvin  and
Gaston Giroux
Brigitte Chauvin*
Affiliation:
Université Paris VI
Gaston Giroux*
Affiliation:
Université de Sherbrooke
*
∗Postal address: Université Paris VI, Laboratoire de Probabilités, 4, Place Jussieu, tour 56, 75230 Paris Cedex 05, France.
∗∗Postal address: Départment de Mathématiques, Université de Sherbrooke, Sherbrooke, Québec, J1K 2R1, Canada.
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Abstract

We construct Boltzmann processes using the formalism of random trees. We are then able to extend previous results about convergence toward the equilibrium law to interactions involving random numbers of particles. We even show a geometric rate of convergence for an extended class of processes, especially for those having a scaling invariant interaction mechanism.

Keywords

BOLTZMANN EQUATIONRANDOM TREE
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 3 , September 1990 , pp. 510 - 520
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

Research supported in part by NSERC, Canada, under Grant No A-5365 and in part by a grant of FCAR, Gouvernement du Québec.

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