A geometric rate of convergence to the equilibrium for Boltzmann processes with multiple particle interactions
- 1 September 1990
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 27 (3) , 510-520
- https://doi.org/10.2307/3214537
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
This publication has 12 references indexed in Scilit:
- The Boltzmann Equation and Its ApplicationsPublished by Springer Nature ,1988
- On the rate of Poisson convergenceMathematical Proceedings of the Cambridge Philosophical Society, 1984
- Poisson Approximations and the Definition of the Poisson ProcessThe American Mathematical Monthly, 1984
- Poisson Approximations and the Definition of the Poisson ProcessThe American Mathematical Monthly, 1984
- quations de type de Boltzmann, spatialement homog nesProbability Theory and Related Fields, 1984
- Rarefied Gas DynamicsPublished by Springer Nature ,1969
- An exponential formula for solving Boltzmann's equation for a Maxwellian gasJournal of Combinatorial Theory, 1967
- Speed of approach to equilibrium for Kac's caricature of a Maxwellian gasArchive for Rational Mechanics and Analysis, 1966
- An approximation theorem for the Poisson binomial distributionPacific Journal of Mathematics, 1960
- On Boltzmann's equation in the kinetic theory of gasesMathematical Proceedings of the Cambridge Philosophical Society, 1951