Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 347, Issue 3, Pages 933-981Publisher
SPRINGER
DOI: 10.1007/s00220-016-2578-y
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Funding
- European Research Council under the European Union / ERC [291147]
- Royal Society
- Hungarian National Science Foundation (OTKA) [K100473]
- Leverhulme Trust through International Network Grant Laplacians, Random Walks, Quantum Spin Systems
- Isaac Newton Institute, Cambridge
- European Research Council (ERC) [291147] Funding Source: European Research Council (ERC)
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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 root t log t, 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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