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

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

2003-09-22

arxiv.org/abs/math/0309359v1

Mathematics

Dynamical Systems

Scientific paper

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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