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April 2016 Quantitative propagation of chaos for generalized Kac particle systems
Roberto Cortez, Joaquin Fontbona
Ann. Appl. Probab. 26(2): 892-916 (April 2016). DOI: 10.1214/15-AAP1107

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.

Citation

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Roberto Cortez. Joaquin Fontbona. "Quantitative propagation of chaos for generalized Kac particle systems." Ann. Appl. Probab. 26 (2) 892 - 916, April 2016. https://doi.org/10.1214/15-AAP1107

Information

Received: 1 June 2014; Revised: 1 February 2015; Published: April 2016
First available in Project Euclid: 22 March 2016

zbMATH: 1339.60138
MathSciNet: MR3476628
Digital Object Identifier: 10.1214/15-AAP1107

Subjects:
Primary: 60K35
Secondary: 82C22, 82C40

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.26 • No. 2 • April 2016
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