Abstract
We prove that, for the planar Lorentz process with a periodic configuration of scatterers, the quasi-local CLT of the gaussian {logϱ n} type holds for any ϱ>1. Consequently, for arbitrary ϱ>3/2, the probabilities that, at the moment of thenth reflection, this process lies in a square of size logϱ n are asymptotically gaussian. This implies that these events occur for infinitely many values ofn (i.e. a weaker form of recurrence).
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Communicated by Ya. G. Sinai
Dedicated to Professor Ya. G. Sinai on the occasion of his 50th birthday
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Krámli, A., Szász, D. The problem of recurrence for Lorentz processes. Commun.Math. Phys. 98, 539–552 (1985). https://doi.org/10.1007/BF01209329
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DOI: https://doi.org/10.1007/BF01209329