Expanding on average diffeomorphisms of surfaces: exponential mixing

TL;DR

This paper proves that certain random dynamical systems on surfaces, built from volume-preserving diffeomorphisms, exhibit exponential mixing, indicating rapid statistical independence over time.

Contribution

It establishes exponential mixing for Bernoulli random dynamical systems generated by expanding on average volume-preserving surface diffeomorphisms, extending understanding of their statistical properties.

Findings

Proves exponential mixing for the considered systems.

Shows Bernoulli random dynamical systems are exponentially mixing.

Extends previous results to a broader class of surface diffeomorphisms.

Abstract

We show that the Bernoulli random dynamical system associated to a expanding on average tuple of volume preserving diffeomorphisms of a closed surface is exponentially mixing.