Large deviations from a kinetic limit

Fraydoun Rezakhanlou

doi:10.1214/aop/1022855753

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Home > Journals > Ann. Probab. > Volume 26 > Issue 3 > Article

July 1998 Large deviations from a kinetic limit

Fraydoun Rezakhanlou

Ann. Probab. 26(3): 1259-1340 (July 1998). DOI: 10.1214/aop/1022855753

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Abstract

We study a one-dimensional particle system in which particles travel deterministically in between stochastic collisions. As the total number of particles tends to infinity, the empirical density converges to a solution of a discrete Boltzmann equation. We establish the large deviation principle for the convergence with a rate function that is given by a variational formula. Some of the properties of the rate function are discussed and a nonvariational expression for the rate function is given.