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

2015/06/11 by Jens Marklof, Marklof, Jens, Bálint Tóth +1
Mathematics · Physics and Astronomy · #37D50 #60F17 #82C40 #Advanced Thermodynamics and Statistical Mechanics #Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1506.03619

openalex publication_date 2015/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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