The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 2 (2016), 892-916.
Quantitative propagation of chaos for generalized Kac particle systems
We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac’s model of the Boltzmann equation and nonlinear equations for the evolution of wealth distribution arising in kinetic economic models. We obtain explicit rates of convergence for the Wasserstein distance between the law of the particles and their limiting law, which are linear in time and depend in a mild polynomial manner on the number of particles. The proof is based on a novel coupling between the particle system and a suitable system of nonindependent nonlinear processes, as well as on recent sharp estimates for empirical measures.
Ann. Appl. Probab., Volume 26, Number 2 (2016), 892-916.
Received: June 2014
Revised: February 2015
First available in Project Euclid: 22 March 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]
Secondary: 82C22: Interacting particle systems [See also 60K35] 82C40: Kinetic theory of gases
Cortez, Roberto; Fontbona, Joaquin. Quantitative propagation of chaos for generalized Kac particle systems. Ann. Appl. Probab. 26 (2016), no. 2, 892--916. doi:10.1214/15-AAP1107. https://projecteuclid.org/euclid.aoap/1458651823