arXiv math/03093592003-09-22math.DS

Local Limit Theorem for the Lorentz Process and Its Recurrence in the Plane

Domokos Szász, Tamás Varjú

发表信息：: Duke Math. J. 148, no. 3 (2009), 459-499
DOI：: 10.1215/00127094-2009-031

英文摘要：

For Young systems, i.e. for hyperbolic systems without/with singularities satisfying Lai-Sang Young's axioms (which imply exponential decay of correlation and the CLT) a local CLT is proven. In fact, a unified version of the local CLT is found, covering among others the absolutely contionuous and the arithmetic cases. For the planar Lorentz process with a finite horizon this result implies a.) the local CLT and b.) the recurrence. For the latter case ($d=2$, finite horizon), combining the global CLT with abstract ergodic theoretic ideas, K. Schmidt, and J.-P. Conze, could already establish recurrence.

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