- 03-438 Domokos Sz\'asz, Tam\'as Varj\'u
- Local Limit Theorem for the Lorentz Process and Its Recurrence in the Plane
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Sep 23, 03
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Abstract. For Young systems, i.e. for hyperbolic systems without/with singularities satisfying 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.