Andras Kramli

Dugonics ter 13, 6720, Szeged, Hungary
University of Szeged, Szeged, Hungary


Kramli A.
The problem of recurrence for the planar Lorentz gas
2003, vol. 8, no. 4, pp.  395-411
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.
Citation: Kramli A.,  The problem of recurrence for the planar Lorentz gas , Regular and Chaotic Dynamics, 2003, vol. 8, no. 4, pp. 395-411

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