Escape Rates Formulae and Metastability for Randomly perturbed maps

TL;DR

This paper develops escape rate formulae for piecewise expanding interval maps with random holes and uses them to approximate invariant densities in metastable systems, advancing understanding of stochastic perturbations.

Contribution

It introduces new escape rate formulae for systems with random holes and applies them to approximate invariant densities in metastable maps.

Findings

Escape rate formulae for maps with random holes

Rigorous approximation of invariant densities

Application to metastable systems

Abstract

We provide escape rates formulae for piecewise expanding interval maps with `random holes'. Then we obtain rigorous approximations of invariant densities of randomly perturbed metabstable interval maps. We show that our escape rates formulae can be used to approximate limits of invariant densities of randomly perturbed metastable systems.