Quantitative Propagation of Chaos for Generalized Kacparticle Systems
Author
dc.contributor.author
Cortez, Roberto
Author
dc.contributor.author
Fontbona Torres, Joaquín
Admission date
dc.date.accessioned
2016-09-29T19:47:09Z
Available date
dc.date.available
2016-09-29T19:47:09Z
Publication date
dc.date.issued
2016
Cita de ítem
dc.identifier.citation
Annals of Applied Probability 2016, Vol. 26, No. 2, 892–916
es_ES
Identifier
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10.1214/15-AAP1107
Identifier
dc.identifier.uri
https://repositorio.uchile.cl/handle/2250/140586
Abstract
dc.description.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.
es_ES
Patrocinador
dc.description.sponsorship
Proyecto Mecesup Doctoral Fellowship
UCH0607
Fondecyt Grant
1110923
Basal-CONICYT Center for Mathematical Modeling (CMM)
Millenium Nucleus
NC120062