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Superdiffusion in the periodic Lorentz gas

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Original languageEnglish
Pages (from-to)933-981
Number of pages49
JournalCommunications in Mathematical Physics
Issue number3
Early online date18 Feb 2016
DateAccepted/In press - 16 Nov 2015
DateE-pub ahead of print - 18 Feb 2016
DatePublished (current) - Nov 2016


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 √tlogt, 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.

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