Propagation of chaos and return to equilibrium for Kac's random walks

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• Clement Mouhot (University of Cambridge)
• Thursday 15 November 2012, 16:00-17:00
• Physics West 103.

If you have a question about this talk, please contact Neal Bez.

Kac proposed in 1956 to study the derivation of the (spatially homogeneous) Boltzmann equation from a many-particle jump processes with random binary collisions (“Kac’s walk”). This limit is closely connected to the notion of propagation of chaos, i.e. product-like structure of the many-particle distribution in the many-particle limit. Several questions were raised: propagation of chaos for the unbounded collision rates encountered in physics, estimations of rates of relaxation uniform in the many-particle limit, propagation of entropic chaos and derivation of the H-theorem. We shall present answers to these questions, obtained in a joint work with Stephane Mischler. They are based on a new quantitative stability approach for many-particle limits, that allows to take advantage of dissipativity of the level of the limit PDE . If time allows we shall discuss connexions with the BBGKY hierarchy, and how this method applies to other many-particle limits.

This talk is part of the Analysis seminar series.

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• Analysis seminar
• Analysis seminar
• Physics West 103
• School of Mathematics events

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