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

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.

References in corpus (2)

• Nonequilibrium Energy Profiles for a Class of 1-D Models
• Typicality of recurrence for Lorentz gases

Cited by in corpus (11)

• A functional analytic approach to perturbations of the Lorentz gas
• New horizons in multidimensional diffusion: The Lorentz gas and the Riemann Hypothesis
• Non equilibrium density profiles in Lorentz tubes with thermostated boundaries
• Locally Perturbed Random Walks with Unbounded Jumps
• Uniformly expanding Markov maps of the real line: exactness and infinite mixing
• Infinite-horizon Lorentz tubes and gases: recurrence and ergodic properties
• Recurrence properties of a special type of Heavy-Tailed Random Walk
• Lorentz Process with shrinking holes in a wall
• Markov partition and Thermodynamic Formalism for Hyperbolic Systems with Singularities
• Random walks and Lorentz processes
• Equidistribution for standard pairs in planar dispersing billiard flows