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

Domokos Szász·Tamás Varjú
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Abstract

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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Domokos Szász, Tamás Varjú. 2003-09-22. Local Limit Theorem for the Lorentz Process and Its Recurrence in the Plane. https://doi.org/10.1215/00127094-2009-031

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