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Funktsional'nyi Analiz i ego Prilozheniya, 2008, Volume 42, Issue 3, Pages 10–22
DOI: https://doi.org/10.4213/faa2909 (Mi faa2909) 		 
This article is cited in 6 scientific papers (total in 6 papers)

The Statistics of Particle Trajectories in the Homogeneous Sinai Problem for a Two-Dimensional Lattice

V. A. Bykovskii, A. V. Ustinov

Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
Full-text PDF (194 kB) Citations (6)
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DOI: https://doi.org/10.4213/faa2909
Abstract: In this paper, we generalize and refine some results by F. P. Boca, R. N. Gologan, and A. Zaharescu on the asymptotic behavior as $h\to 0$ of the statistics of the free path length until the first hit of the $h$-neighborhood (a disk of radius $h$) of a nonzero integer for a particle issuing from the origin. The established facts imply that the limit distribution function for the free path length and for the sighting parameter (the distance from the trajectory to the integer point in question) does not depend on the particle escape direction (the property of isotropy).
Keywords: integer lattice, continued fraction, Kloosterman's sum.
Received: 24.01.2007
English version:
Functional Analysis and Its Applications, 2008, Volume 42, Issue 3, Pages 169–179
DOI: https://doi.org/10.1007/s10688-008-0026-2
Bibliographic databases:
Document Type: Article
UDC: 511.336+511.9+517.987.5
Language: Russian
Citation: V. A. Bykovskii, A. V. Ustinov, “The Statistics of Particle Trajectories in the Homogeneous Sinai Problem for a Two-Dimensional Lattice”, Funktsional. Anal. i Prilozhen., 42:3 (2008), 10–22; Funct. Anal. Appl., 42:3 (2008), 169–179
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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