We introduce a Kac’s type walk whose rate of binary collisions preserves the total momentum but not the kinetic energy. In the limit of large number of particles we describe the dynamics in terms of empirical measure and flow, proving the corresponding large deviation principle. The associated rate function has an explicit expression. As a byproduct of this analysis, we provide a gradient flow formulation of the Boltzmann-Kac equation.
Large Deviations for Kac-Like Walks / Basile, G.; Benedetto, D.; Bertini, L.; Orrieri, C.. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - 184:1(2021). [10.1007/s10955-021-02794-2]
Large Deviations for Kac-Like Walks
Basile G.;Benedetto D.
;Bertini L.;
2021
Abstract
We introduce a Kac’s type walk whose rate of binary collisions preserves the total momentum but not the kinetic energy. In the limit of large number of particles we describe the dynamics in terms of empirical measure and flow, proving the corresponding large deviation principle. The associated rate function has an explicit expression. As a byproduct of this analysis, we provide a gradient flow formulation of the Boltzmann-Kac equation.| File | Dimensione | Formato | |
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