The Annals of Applied Probability

Quantitative propagation of chaos for generalized Kac particle systems

Roberto Cortez and Joaquin Fontbona

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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.

Article information

Ann. Appl. Probab., Volume 26, Number 2 (2016), 892-916.

Received: June 2014
Revised: February 2015
First available in Project Euclid: 22 March 2016

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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

Propagation of chaos Kac equation wealth distribution equations stochastic particle systems Wasserstein distance optimal coupling


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.

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