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1 April 2008 Recurrence properties of planar Lorentz process
Dmitry Dolgopyat, Domokos Szász, Tamás Varjú
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Duke Math. J. 142(2): 241-281 (1 April 2008). DOI: 10.1215/00127094-2008-006

Abstract

First-return and first-hitting times, local times, and first-intersection times are studied for planar finite-horizon Lorentz processes with a periodic configuration of scatterers. Their asymptotic behavior is analogous to the asymptotic behavior of the same quantities for the two-dimensional simple symmetric random walk (see classical results of Darling and Kac [DK] and Erdős and Taylor [ET]. Moreover, asymptotical distributions for phases in first hittings and in first intersections of Lorentz processes are also proved. The results are also extended to the quasi-one-dimensional model of the linear Lorentz process

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Dmitry Dolgopyat. Domokos Szász. Tamás Varjú. "Recurrence properties of planar Lorentz process." Duke Math. J. 142 (2) 241 - 281, 1 April 2008. https://doi.org/10.1215/00127094-2008-006

Information

Published: 1 April 2008
First available in Project Euclid: 27 March 2008

zbMATH: 1136.37022
MathSciNet: MR2401621
Digital Object Identifier: 10.1215/00127094-2008-006

Subjects:
Primary: 37D50 , 60F05

Rights: Copyright © 2008 Duke University Press

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Vol.142 • No. 2 • 1 April 2008
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