Kac’s chaos and Kac’s program

Stéphane Mischler[1]

  • [1] Université Paris-Dauphine & IUF CEREMADE, UMR CNRS 7534 Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16 France

Séminaire Laurent Schwartz — EDP et applications (2012-2013)

  • Volume: 2012-2013, page 1-17
  • ISSN: 2266-0607

Abstract

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In this note I present the main results about the quantitative and qualitative propagation of chaos for the Boltzmann-Kac system obtained in collaboration with C. Mouhot in [33] which gives a possible answer to some questions formulated by Kac in [25]. We also present some related recent results about Kac’s chaos and Kac’s program obtained in [34, 23, 13] by K. Carrapatoso, M. Hauray, C. Mouhot, B. Wennberg and myself.

How to cite

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Mischler, Stéphane. "Kac’s chaos and Kac’s program." Séminaire Laurent Schwartz — EDP et applications 2012-2013 (2012-2013): 1-17. <http://eudml.org/doc/275761>.

@article{Mischler2012-2013,
abstract = {In this note I present the main results about the quantitative and qualitative propagation of chaos for the Boltzmann-Kac system obtained in collaboration with C. Mouhot in [33] which gives a possible answer to some questions formulated by Kac in [25]. We also present some related recent results about Kac’s chaos and Kac’s program obtained in [34, 23, 13] by K. Carrapatoso, M. Hauray, C. Mouhot, B. Wennberg and myself.},
affiliation = {Université Paris-Dauphine & IUF CEREMADE, UMR CNRS 7534 Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16 France},
author = {Mischler, Stéphane},
journal = {Séminaire Laurent Schwartz — EDP et applications},
keywords = {Kac's program; Kac's chaos; kinetic theory; master equation; mean-field limit; jump process; collision process; Boltzmann equation; Maxwell molecules; non cutoff; hard spheres; Monge-Kantorovich-Wasserstein distance; entropy chaos; Fisher information chaos; CLT with optimal rate; quantitative chaos; qualitative chaos; uniform in time},
language = {eng},
pages = {1-17},
publisher = {Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Kac’s chaos and Kac’s program},
url = {http://eudml.org/doc/275761},
volume = {2012-2013},
year = {2012-2013},
}

TY - JOUR
AU - Mischler, Stéphane
TI - Kac’s chaos and Kac’s program
JO - Séminaire Laurent Schwartz — EDP et applications
PY - 2012-2013
PB - Institut des hautes études scientifiques & Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2012-2013
SP - 1
EP - 17
AB - In this note I present the main results about the quantitative and qualitative propagation of chaos for the Boltzmann-Kac system obtained in collaboration with C. Mouhot in [33] which gives a possible answer to some questions formulated by Kac in [25]. We also present some related recent results about Kac’s chaos and Kac’s program obtained in [34, 23, 13] by K. Carrapatoso, M. Hauray, C. Mouhot, B. Wennberg and myself.
LA - eng
KW - Kac's program; Kac's chaos; kinetic theory; master equation; mean-field limit; jump process; collision process; Boltzmann equation; Maxwell molecules; non cutoff; hard spheres; Monge-Kantorovich-Wasserstein distance; entropy chaos; Fisher information chaos; CLT with optimal rate; quantitative chaos; qualitative chaos; uniform in time
UR - http://eudml.org/doc/275761
ER -

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