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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2003, том 8, выпуск 4, страницы 395–411 (Mi rcd791)

Эта публикация цитируется в 2 статьях

The problem of recurrence for the planar Lorentz gas

A. Krámli

University of Szeged 6720 Szeged, Hungary

Аннотация: This paper is a brief survey of solving the problem of the recurrence for planar Lorentz process. There are two different ways to do this.
1. Using Lai-Sang Young's construction [27] one proves the local central limit theorem from which Pólya's theorem is then deduced — this is the method of D.Szász and T.Varjú [25].
2. Klaus Schmidt [21] and J.-P.Conze [8] proved that the recurrence of the planar Lorentz process follows from the global central limit theorem, established by Bunimovich and Sinai [7]. The history of the problem and the main ingredients of the proofs are given. The details of K.Schmidt's method are analysed in the Appendix written by V.Bognár.

MSC: 37A50, 37A60, 82C22

Поступила в редакцию: 12.09.2003

Язык публикации: английский

DOI: 10.1070/RD2003v008n04ABEH000253



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