Metastable limit theorems in chaotic dynamical systems

Date: Tuesday 12th August 2025

Abstract

A metastable state is a state which is not a real stable state, but can be observed for a long time. This is a concept that appears in several areas of natural science, like chemical kinetics, meteorology, neuroscience, etc. Some of these phenomena can be modeled as a dynamical system, but traditional dynamical systems theory was developed by analyzing behaviors of the system in the infinite time limit, so mathematical theory for understanding (non-trivial) dynamics on metastable time scales would still not be fully developed (although there are several important developments recently).
In this talk, I try to concentrate on a (famous) toy model dynamics, which is a piecewise expanding interval map without statistical stability (i.e. its "physical" invariant measure does not vary continuously under perturbations), to make the presentation of our idea/formulation transparent. Our results include strong laws of large numbers, central limit theorems with Berry-Esseen type error estimates, large deviation principles on metastable time scales. This is based on joint works in progress with J. Atnip, C. Gonzalez-Tokman, G. Froyland, and S. Vaienti.