Quantitative propagation of chaos for generalized Kac particle systems
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.
Keywords
Cite
@article{arxiv.1406.2115,
title = {Quantitative propagation of chaos for generalized Kac particle systems},
author = {Roberto Cortez and Joaquin Fontbona},
journal= {arXiv preprint arXiv:1406.2115},
year = {2016}
}
Comments
Published at http://dx.doi.org/10.1214/15-AAP1107 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)