Limit Theorems for Fast-slow partially hyperbolic systems

TL;DR

This paper establishes new limit theorems for a class of partially hyperbolic fast-slow systems, including refined deviation results and a novel local limit theorem, using advanced probabilistic and dynamical systems techniques.

Contribution

It provides a substantial refinement of large and moderate deviation results and introduces a new local limit theorem for these systems, with a versatile proof method.

Findings

Refined large deviation estimates for fast-slow systems

A new local limit theorem for fluctuation distributions

Method combining standard pairs and Transfer Operators

Abstract

We prove several limit theorems for a simple class of partially hyperbolic fast-slow systems. We start with some well know results on averaging, then we give a substantial refinement of known large (and moderate) deviation results and conclude with a completely new result (a local limit theorem) on the distribution of the process determined by the fluctuations around the average. The method of proof is based on a mixture of standard pairs and Transfer Operators that we expect to be applicable in a much wider generality.