%0 Journal Article %1 cortez2015quantitative %A Cortez, Roberto %A Fontbona, Joaquin %D 2015 %K particle-system %T Quantitative uniform propagation of chaos for Maxwell molecules %U http://arxiv.org/abs/1512.09308 %X We prove propagation of chaos at explicit polynomial rates in Wasserstein distance W_2 for Kac's N-particle system associated with the spatially homogeneous Boltzmann equation for Maxwell molecules, with and without cutoff. Our approach is mainly based on novel probabilistic coupling techniques. Combining them with recent stabilization results for the particle system we obtain, under suitable moments assumptions on the initial distribution, a uniform-in-time estimate of order almost N^-1/3 for W_2^2.

@article{cortez2015quantitative, abstract = {We prove propagation of chaos at explicit polynomial rates in Wasserstein distance W_2 for Kac's N-particle system associated with the spatially homogeneous Boltzmann equation for Maxwell molecules, with and without cutoff. Our approach is mainly based on novel probabilistic coupling techniques. Combining them with recent stabilization results for the particle system we obtain, under suitable moments assumptions on the initial distribution, a uniform-in-time estimate of order almost N^{-1/3} for W_2^2.}, added-at = {2017-12-27T20:52:41.000+0100}, author = {Cortez, Roberto and Fontbona, Joaquin}, biburl = {https://www.bibsonomy.org/bibtex/288f624c07fd99707d5953ce705da28d6/claired}, description = {Quantitative uniform propagation of chaos for Maxwell molecules}, interhash = {1bc808f6f29aaf779b80eb701d942dc2}, intrahash = {88f624c07fd99707d5953ce705da28d6}, keywords = {particle-system}, note = {cite arxiv:1512.09308Comment: 28 pages. This version is accepted for publication in Communications in Mathematical Physics}, timestamp = {2017-12-27T20:52:41.000+0100}, title = {Quantitative uniform propagation of chaos for Maxwell molecules}, url = {http://arxiv.org/abs/1512.09308}, year = 2015 }