Polynomial decay of correlations for flows, including Lorentz gas examples

TL;DR

This paper establishes precise polynomial decay rates of correlations for certain nonuniformly hyperbolic flows, with applications to models like Lorentz gases, enhancing understanding of their statistical properties.

Contribution

It provides sharp decay estimates for correlations in nonuniform hyperbolic flows, including Lorentz gas models, extending previous results to more general settings.

Findings

Polynomial decay rates are proven for a class of flows.

Applications include Lorentz gas models with infinite horizon.

Results improve understanding of statistical properties of these systems.

Abstract

We prove sharp results on polynomial decay of correlations for nonuniformly hyperbolic flows. Applications include intermittent solenoidal flows and various Lorentz gas models including the infinite horizon Lorentz gas.