Uniform Propagation of Chaos for Kac’s 1D Particle System

Resultado de la investigación: Article

Resumen

In this paper we study Kac’s 1D particle system, consisting of the velocities of N particles colliding at constant rate and randomly exchanging energies. We prove uniform (in time) propagation of chaos in Wasserstein distance with explicit polynomial rates in N, for both the squared (i.e., the energy) and non-squared particle system. These rates are of order N- 1 / 3 (almost, in the non-squared case), assuming that the initial distribution of the limit nonlinear equation has finite moments of sufficiently high order (4 + ϵ is enough when using the 2-Wasserstein distance). The proof relies on a convenient parametrization of the collision recently introduced by Hauray, as well as on a coupling technique developed by Cortez and Fontbona.

Idioma originalEnglish
Páginas (desde-hasta)1102-1113
Número de páginas12
PublicaciónJournal of Statistical Physics
Volumen165
N.º6
DOI
EstadoPublished - 1 dic 2016

Huella dactilar

Propagation of Chaos
Wasserstein Distance
Particle System
chaos
propagation
Energy
Rate Constant
Parametrization
Nonlinear Equations
exchanging
Collision
Higher Order
Moment
nonlinear equations
Polynomial
polynomials
moments
collisions
energy

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Citar esto

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Uniform Propagation of Chaos for Kac’s 1D Particle System. / Cortez, Roberto.

En: Journal of Statistical Physics, Vol. 165, N.º 6, 01.12.2016, p. 1102-1113.

Resultado de la investigación: Article

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AB - In this paper we study Kac’s 1D particle system, consisting of the velocities of N particles colliding at constant rate and randomly exchanging energies. We prove uniform (in time) propagation of chaos in Wasserstein distance with explicit polynomial rates in N, for both the squared (i.e., the energy) and non-squared particle system. These rates are of order N- 1 / 3 (almost, in the non-squared case), assuming that the initial distribution of the limit nonlinear equation has finite moments of sufficiently high order (4 + ϵ is enough when using the 2-Wasserstein distance). The proof relies on a convenient parametrization of the collision recently introduced by Hauray, as well as on a coupling technique developed by Cortez and Fontbona.

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