### 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 original | English |
---|---|

Páginas (desde-hasta) | 1102-1113 |

Número de páginas | 12 |

Publicación | Journal of Statistical Physics |

Volumen | 165 |

N.º | 6 |

DOI | |

Estado | Published - 1 dic 2016 |

### Huella dactilar

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

### Citar esto

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*Journal of Statistical Physics*, vol. 165, n.º 6, pp. 1102-1113. https://doi.org/10.1007/s10955-016-1674-x

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

Resultado de la investigación: Article

TY - JOUR

T1 - Uniform Propagation of Chaos for Kac’s 1D Particle System

AU - Cortez, Roberto

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

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.

KW - Kac particle system

KW - Kinetic theory

KW - Propagation of chaos

UR - http://www.scopus.com/inward/record.url?scp=85028256773&partnerID=8YFLogxK

U2 - 10.1007/s10955-016-1674-x

DO - 10.1007/s10955-016-1674-x

M3 - Article

AN - SCOPUS:85028256773

VL - 165

SP - 1102

EP - 1113

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

SN - 0022-4715

IS - 6

ER -