Pointwise estimates and exponential laws in metastable systems via coupling methods

TL;DR

This paper employs coupling techniques to analyze metastable systems, demonstrating that mean exit times are nearly constant within certain states and establishing the exponential distribution of escape times in the Random Field Curie Weiss model.

Contribution

It introduces coupling methods to prove near-constancy of metastable exit times and their exponential distribution in specific models.

Findings

Mean metastable exit times are almost constant within a meta-stable set.

Normalized escape times follow an asymptotic exponential law.

Coupling techniques effectively analyze metastable behaviors.

Abstract

We show how coupling techniques can be used in some metastable systems to prove that mean metastable exit times are almost constant as functions of the starting microscopic configuration within a "meta-stable set." In the example of the Random Field Curie Weiss model, we show that these ideas can also be used to prove asymptotic exponentiallity of normalized metastable escape times.