Central Limit Theorem for a Class of Billiards

Abstract

Previous article Next article Central Limit Theorem for a Class of BilliardsL. A. BunimovicL. A. Bunimovichttps://doi.org/10.1137/1119006PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] L. A. Bunimovič, The ergodic properties of billiards that are nearly scattering, Dokl. Akad. Nauk SSSR, 211 (1973), 1024–1026, (In Russian.) MR0330413 (48:8750) Google Scholar[2] A. N. Kolmogorov, A new metric invariant of transient dynamical systems and automorphisms in Lebesgue spaces, Dokl. Akad. Nauk SSSR (N.S.), 119 (1958), 861–864, (In Russian.) MR0103254 (21:2035a) 0083.10602 Google Scholar[3] V. A. Rokhlin, Recent progress in the theory of transformations with invariant measure, Uspekhi Mat. Nauk., 15 (1960), 3–26, (In Russian.) Google Scholar[4] Ja. G. Sinai˘, Dynamical systems with elastic reflections. Ergodic properties of dispersing billiards, Uspehi Mat. Nauk, 25 (1970), 141–192, (In Russian.) MR0274721 (43:481) Google Scholar[5] L. A. Bunimovich, A central limit theorem for scattering billiards, Dokl. Akad. Nauk SSSR, 204 (1972), 778–781 MR0301167 (46:325) Google Scholar[6] V. A. Rokhlin, On the basic concepts of measure theory, Mat. Sb., 25 (67) (1949), 107–150, (In Russian.) Google Scholar[7] L. A. Bunimovich and , Ya. G. Sinai, The fundamental theorem of the theory of scattering billiards, Mat. Sb. (N.S.), 90(132) (1973), 415–431, 479, (In Russian.) MR0367153 (51:3395) Google Scholar[8] Ya. G. Sinai, Classical dynamic systems with countably-multiple Lebesgue spectrum. II, Izv. Akad. Nauk SSSR Ser. Mat., 30 (1966), 15–68 MR0197684 (33:5847) Google Scholar[9] D. V. Anosov, Geodesic flows on closed Riemannian manifolds of negative curvature, Trudy Mat. Inst. Steklov., 90 (1967), 209–, “Nauka”, Moscow, (In Russian.) MR0224110 (36:7157) Google Scholar[10] D. V. Anosov and , ya. G. Sinai, Certain smooth ergodic systems, Uspehi Mat. Nauk, 22 (1967), 107–172, (In Russian.) MR0224771 (37:370) 0177.42002 Google Scholar[11] Ya. G. Sinai, Central limit theorem for geodesic flows on manifolds of constant negative curvature, Dokl. Akad. Nauk SSSR, 133 (1960), 1303–1306, (In Russian.) Google Scholar[12] Ya. G. Sinai, Candidate's Dissertation, Moscow State Univ., 1960 Google Scholar[13] Ya. G. Sinai, On limit theorems for stationary processes, Theory Prob. Applications, 7 (1962), 205–210 10.1137/1107021 0115.35804 LinkGoogle Scholar[14] M. Rosenblatt, A central limit theorem and a strong mixing condition, Proc. Nat. Acad. Sci. U. S. A., 42 (1956), 43–47 MR0074711 (17,635b) 0070.13804 CrossrefGoogle Scholar[15] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– MR0322926 (48:1287) 0219.60027 Google Scholar[16] B. V. Gnedenko and , A. N. Kolmogorov, Limit distributions for sums of independent random variables, Addison-Wesley Publishing Company, Inc., Cambridge, Mass., 1954ix+264 MR0062975 (16,52d) 0056.36001 Google Scholar[17] V. P. Leonov, Applications of Higher Order Cumulants to the Theory of Stationary Stochastic Processes, Nauka, Moscow, 1964, (In Russian.) Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Dynamical systems with time scale separation: averaging, stochastic modelling, and central limit theorems Cross Ref Approach to Gaussian stochastic behavior for systems driven by deterministic chaotic forces1 November 1999 | Physical Review E, Vol. 60, No. 5 Cross Ref Dynamical systems of Langevin typePhysica A: Statistical Mechanics and its Applications, Vol. 233, No. 1-2 Cross Ref Brownian motion from deterministic dynamicsPhysica A: Statistical Mechanics and its Applications, Vol. 169, No. 2 Cross Ref Transport properties of stochastic Lorentz models1 January 1982 | Reviews of Modern Physics, Vol. 54, No. 1 Cross Ref Long-time correlation effects on displacement distributionsJournal of Statistical Physics, Vol. 19, No. 4 Cross Ref Lecture VIII a model for couette flow data27 August 2006 Cross Ref Computer results on transport properties Cross Ref Volume 19, Issue 1| 1974Theory of Probability & Its Applications History Submitted:26 January 1973Published online:28 July 2006 InformationCopyright © 1974 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1119006Article page range:pp. 65-85ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics