Metastability of random maps: a resolvent approach

TL;DR

This paper introduces a comprehensive framework combining Markov process theory and spectral analysis to study metastability in randomly perturbed dynamical systems, with applications to one-dimensional maps affected by sub-Gaussian noise.

Contribution

It develops a novel resolvent-based approach that unifies spectral and probabilistic methods for analyzing metastability in stochastic dynamical systems.

Findings

Framework effectively characterizes metastable states.

Application to one-dimensional maps demonstrates practical utility.

Spectral analysis reveals detailed metastability structure.

Abstract

We present a general framework to study the metastability of random perturbations of dynamical systems. It integrates techniques from the theory of Markov processes, in particular the resolvent approach to metastability, with the spectral analysis of transfer operators associated to the dynamics. The proposed framework is applied to study the metastability of one-dimensional dynamical systems generated by a map randomly perturbed by sub-Gaussian noise.