Abstract
We prove scaling to nondegenerate Brownian motion for the path of a test particle in the stochastic Lorentz lattice gas on ℤd under a weak ergodicity assumption on the scatterer distribution. We prove that recurrence holds almost surely ind⩽2. Transience ind⩾3 remains open.
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den Hollander, F., Naudts, J. & Redig, F. Invariance principle for the stochastic Lorentz lattice gas. J Stat Phys 66, 1583–1598 (1992). https://doi.org/10.1007/BF01054435
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DOI: https://doi.org/10.1007/BF01054435