|
This article is cited in 2 scientific papers (total in 2 papers)
The problem of recurrence for the planar Lorentz gas
A. Krámli University of Szeged 6720 Szeged, Hungary
Abstract:
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.
Received: 12.09.2003
Citation:
A. Krámli, “The problem of recurrence for the planar Lorentz gas”, Regul. Chaotic Dyn., 8:4 (2003), 395–411
Linking options:
https://www.mathnet.ru/eng/rcd791 https://www.mathnet.ru/eng/rcd/v8/i4/p395
|
Statistics & downloads: |
Abstract page: | 52 |
|