Rare events, escape rates and quasistationarity: some exact formulae

TL;DR

This paper introduces a unified framework for analyzing decay and exchange rates in various dynamical systems, with applications spanning continued fractions, constrained systems, and metastable states.

Contribution

It provides exact formulae for decay rates and quasistationary behavior across a broad class of dynamical systems, unifying multiple applications.

Findings

Derived exact formulae for escape rates in dynamical systems

Applied framework to continued fractions and constrained systems

Analyzed decay rates of metastable states

Abstract

We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging form the metric theory of continuons fractions and the Shannon capacity of contrained systems to the decay rate of metastable states, are given.