Local large deviations for periodic infinite horizon Lorentz gases

TL;DR

This paper establishes local large deviation principles for periodic infinite horizon Lorentz gases and extends these results to a broader class of nonuniformly hyperbolic dynamical systems with nonstandard CLT normalizations.

Contribution

It provides the first local large deviation results for infinite horizon Lorentz gases and generalizes the theory to nonuniformly hyperbolic systems with nonstandard CLT scaling.

Findings

Proved local large deviations for periodic infinite horizon Lorentz gases.

Extended large deviation results to a class of nonuniformly hyperbolic systems.

Applicable to observables associated with nonstandard CLTs.

Abstract

We prove local large deviations for the periodic infinite horizon Lorentz gas viewed as a ${\mathbb Z}^d$-cover ($d=1,2$) of a dispersing billiard. In addition to this specific example, we prove a general result for a class of nonuniformly hyperbolic dynamical systems and observables associated with central limit theorems with nonstandard normalisation.