Invariance principle for the periodic Lorentz gas in the Boltzmann-Grad limit

Publication date: 11 June 2015

Abstract: In earlier work we showed that the particle displacement for the multidimensional periodic Lorentz gas, in the limit of low scatterer density (Boltzmann-Grad limit), satisfies a central limit theorem with superdiffusive scaling. The present paper extends this result to a functional central limit theorem, i.e., the weak convergence of the particle trajectory to Brownian motion.

Mathematics Subject Classification ID

Kinetic theory of gases in time-dependent statistical mechanics (82C40) Functional limit theorems; invariance principles (60F17)

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