Superdiffusion in the periodic Lorentz gas

DOI10.1007/S00220-016-2578-YzbMATH Open1368.37018arXiv1403.6024OpenAlexW2964292971WikidataQ59477155 ScholiaQ59477155MaRDI QIDQ330897

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Publication date: 26 October 2016

Published in: (Search for Journal in Brave)

Abstract: We prove a superdiffusive central limit theorem for the displacement of a test particle in the periodic Lorentz gas in the limit of large times $t$ and low scatterer densities (Boltzmann-Grad limit). The normalization factor is $sqrttlogt$, where $t$ is measured in units of the mean collision time. This result holds in any dimension and for a general class of finite-range scattering potentials. We also establish the corresponding invariance principle, i.e., the weak convergence of the particle dynamics to Brownian motion.

Full work available at URL: https://arxiv.org/abs/1403.6024

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