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Article
Spectral analysis of the transfer operator for the Lorentz gas
Journal of Modern Dynamics
  • Mark Demers, Fairfield University
  • Hong-Kun Zhang
Document Type
Article
Article Version
Publisher's PDF
Publication Date
1-1-2011
Abstract
We study the billiard map associated with both the finite and infinite horizon Lorentz gases having smooth scatterers with strictly positive curvature. We introduce generalized function spaces (Banach spaces of distributions) on which the transfer operator is quasi-compact. The mixing properties of the billiard map then imply the existence of a spectral gap and related statistical properties such as exponential decay of correlations and the central limit theorem. Finer statistical properties of the map such as the identification of Ruelle resonances, large deviation estimates and an almost-sure invariance principle follow immediately once the spectral picture is established.
Comments

Copyright 2011 American Institute of Mathematical Sciences, Journal of Modern Dynamics.

Published Citation
Mark Demers and Hong-Kun Zhang, "Spectral analysis of the transfer operator for the Lorentz gas." Journal of Modern Dynamics 5:4 (2011), 665-709.
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Peer Reviewed
Citation Information
Mark Demers and Hong-Kun Zhang. "Spectral analysis of the transfer operator for the Lorentz gas" Journal of Modern Dynamics Vol. 5 Iss. 4 (2011)
Available at: http://works.bepress.com/mark_demers/4/