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    Dolgopyat, Dmitry and Nándori, Péter 2016. Nonequilibrium Density Profiles in Lorentz Tubes with Thermostated Boundaries. Communications on Pure and Applied Mathematics, Vol. 69, Issue. 4, p. 649.


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    Pène, Françoise and Saussol, Benoît 2010. Back to Balls in Billiards. Communications in Mathematical Physics, Vol. 293, Issue. 3, p. 837.


    Sinai, Y. G. 2010. Chaos Theory Yesterday, Today and Tomorrow. Journal of Statistical Physics, Vol. 138, Issue. 1-3, p. 2.


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    REY-BELLET, LUC and YOUNG, LAI-SANG 2008. Large deviations in non-uniformly hyperbolic dynamical systems. Ergodic Theory and Dynamical Systems, Vol. 28, Issue. 02,


    Szász, Domokos and Varjú, Tamás 2007. Limit Laws and Recurrence for the Planar Lorentz Process with Infinite Horizon. Journal of Statistical Physics, Vol. 129, Issue. 1, p. 59.


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  • Ergodic Theory and Dynamical Systems, Volume 24, Issue 1
  • February 2004, pp. 257-278

Local limit theorem for the Lorentz process and its recurrence in the plane

  • DOMOKOS SZÁSZ (a1) and TAMÁS VARJÚ (a1)
  • DOI: http://dx.doi.org/10.1017/S0143385703000439
  • Published online: 01 February 2004
Abstract

For Young systems, i.e. for hyperbolic systems without/with singularities satisfying Young's axioms (Lai-Sang Young, Ann. Math.147 (1998), 585–650), which imply exponential decay of correlations and the central limit theorem (CLT), a local CLT is proven. In fact, a unified version of the local CLT is found, covering, among others, the absolutely continuous and arithmetic cases. For planar Lorentz process with a finite horizon, this result implies (a) a local CLT and (b) recurrence. For the latter case (d = 2, finite horizon), combining the global CLT with abstract ergodic theoretic ideas, K. Schmidt (C. R. Acad. Sci. Paris Ser. 1 Math. 372(9) (1998), 837–842) and J.-P. Conze (Ergod. Th. & Dynam. Sys.19(5) (1999), 1233–1245) could already establish recurrence.

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Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
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