Determination of the Spectral Gap for Kac's Master Equation and Related Stochastic Evolutions

Details Determination of the Spectral Gap for Kac's Master Equation and Related Stochastic Evolutions Determination of the Spectral Gap for Kac's Master Equation and Related Stochastic Evolutions

2001-09-03

arxiv.org/abs/math-ph/0109003v1

Physics

Mathematical Physics

Plain TeX, 49 pages

Scientific paper

We present a method for bounding, and in some cases computing, the spectral gap for systems of many particles evolving under the influence of a random collision mechanism. In particular, the method yields the exact spectral gap in a model due to Mark Kac of energy conserving collisions with one dimensional velocities. It is also sufficiently robust to provide qualitatively sharp bounds also in the case of more physically realistic momentum and energy conserving collisions in three dimensions, as well as a range of related models.

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