Dugonics ter 13, 6720, Szeged, Hungary
University of Szeged, Szeged, Hungary
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  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 .
2. Klaus Schmidt  and J.-P.Conze  proved that the recurrence of the planar Lorentz process follows from the global central limit theorem, established by Bunimovich and Sinai .
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.