The Annals of Applied Probability

Quantitative propagation of chaos for generalized Kac particle systems

Roberto Cortez and Joaquin Fontbona

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1458651823

Digital Object Identifier
doi:10.1214/15-AAP1107

Mathematical Reviews number (MathSciNet)
MR3476628

Zentralblatt MATH identifier
1339.60138

Subjects
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

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

Citation

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


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