Statistical properties of coupled expanding maps on a lattice with general infinite range couplings and H\"older densities

TL;DR

This paper develops transfer operator techniques for coupled expanding maps on a lattice with general interactions, establishing spectral gaps and proving statistical properties like decay of correlations and the central limit theorem.

Contribution

It extends transfer operator methods to systems with infinite-range couplings and proves key statistical properties for these complex lattice systems.

Findings

Existence of a spectral gap for the transfer operator.

Proof of exponential decay of correlations.

Establishment of the central limit theorem and invariance principles.

Abstract

We continue the development of transfer operator techniques for expanding maps on a lattice coupled by general interaction functions. We obtain a spectral gap for an appropriately defined transfer operator, and, as corollaries, the existence of an invariant conformal probability measure for the system, exponential decay of correlations, the central limit theorem and the almost sure invariance principle.