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October 2008 Propagation of chaos and Poincaré inequalities for a system of particles interacting through their cdf
Benjamin Jourdain, Florent Malrieu
Ann. Appl. Probab. 18(5): 1706-1736 (October 2008). DOI: 10.1214/07-AAP513

Abstract

In this paper, in the particular case of a concave flux function, we are interested in the long time behavior of the nonlinear process associated in [Methodol. Comput. Appl. Probab. 2 (2000) 69–91] to the one-dimensional viscous scalar conservation law. We also consider the particle system obtained by replacing the cumulative distribution function in the drift coefficient of this nonlinear process by the empirical cumulative distribution function. We first obtain a trajectorial propagation of chaos estimate which strengthens the weak convergence result obtained in [8] without any convexity assumption on the flux function. Then Poincaré inequalities are used to get explicit estimates concerning the long time behavior of both the nonlinear process and the particle system.

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Benjamin Jourdain. Florent Malrieu. "Propagation of chaos and Poincaré inequalities for a system of particles interacting through their cdf." Ann. Appl. Probab. 18 (5) 1706 - 1736, October 2008. https://doi.org/10.1214/07-AAP513

Information

Published: October 2008
First available in Project Euclid: 30 October 2008

zbMATH: 1185.65013
MathSciNet: MR2462546
Digital Object Identifier: 10.1214/07-AAP513

Subjects:
Primary: 35K15, 46N30, 60E15, 60K35, 65C35

Rights: Copyright © 2008 Institute of Mathematical Statistics

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Vol.18 • No. 5 • October 2008
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