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15 June 2009 Limit theorems for locally perturbed planar Lorentz processes
Dmitry Dolgopyat, Domokos Szász, Tamás Varjú
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Duke Math. J. 148(3): 459-499 (15 June 2009). DOI: 10.1215/00127094-2009-031

Abstract

Let us modify the scatterer configuration of a planar, finite-horizon Lorentz process in a bounded domain. Sinai asked in 1981 whether, for the diffusively scaled variant of the modified process, convergence to Brownian motion still holds. The main result of this work answers Sinai's question in the affirmative. Other types of local perturbations are also investigated: finite-horizon periodic Lorentz processes in the half strip or in the half plane (in these models, the local perturbation is the boundary condition) and finite-horizon, periodic Lorentz processes with a small, compactly supported external field in the strip. The corresponding limiting processes are Brownian motions with suitable boundary conditions and the skew Brownian motion on the line. The proofs combine Stroock and Varadhan's martingale method in [SV1] with our recent work in [DSV]

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Dmitry Dolgopyat. Domokos Szász. Tamás Varjú. "Limit theorems for locally perturbed planar Lorentz processes." Duke Math. J. 148 (3) 459 - 499, 15 June 2009. https://doi.org/10.1215/00127094-2009-031

Information

Published: 15 June 2009
First available in Project Euclid: 18 June 2009

zbMATH: 1177.37042
MathSciNet: MR2527323
Digital Object Identifier: 10.1215/00127094-2009-031

Subjects:
Primary: 37D50
Secondary: 60F05

Rights: Copyright © 2009 Duke University Press

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Vol.148 • No. 3 • 15 June 2009
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