Quantitative propagation of chaos for generalized kac particle systems

Roberto Cortez, Joaquin Fontbona

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We study a class of one-dimensional particle systems with true (Bird type) binary interactions, which includes Kac'smodel 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.

Original languageEnglish
Pages (from-to)892-916
Number of pages25
JournalAnnals of Applied Probability
Volume26
Issue number2
DOIs
Publication statusPublished - Apr 2016

Keywords

  • Kac equation
  • Optimal coupling
  • Propagation of chaos
  • Stochastic particle systems
  • Wasserstein distance
  • Wealth distribution equations

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint

Dive into the research topics of 'Quantitative propagation of chaos for generalized kac particle systems'. Together they form a unique fingerprint.

Cite this