Exponential decay of random correlations for random Anosov systems mixing on fibers

TL;DR

This paper proves that for certain Anosov systems with mixing properties, the random correlations decay exponentially, enhancing understanding of their statistical behavior under external forces.

Contribution

It establishes exponential decay of quenched random correlations for Anosov systems with mixing on fibers using the Birkhoff cone method, a novel application in this context.

Findings

Exponential decay of random correlations for the systems studied.

Validation of the Birkhoff cone method in this setting.

Results applicable to systems with external forces and mixing properties.

Abstract

In this paper, we study the statistical property of Anosov systems on surface driven by an external force. By utilizing the Birkhoff cone method, we show that if the systems on surface satisfying the Anosov and topological mixing on fibers property, then the quenched random correlation for Holder observables with respect to the unique random SRB measures decays exponentially.