Speaker: Giuseppe Tenaglia
Title: Metastability and conditioned dynamics in high-dimensional systems
Abstract: High-dimensional systems can exhibit long-lived transient behaviour, even when they have a unique invariant measure. In some mean-field models, these metastable regimes correspond to distinct equilibria of the infinite-particle limit, yet the invariant measure of the finite-dimensional system does not capture their transient dynamics. In this talk, we propose quasi-stationary measures as a framework for describing these metastable regimes. These measures are invariant under dynamics conditioned on remaining within a prescribed region, and describe statistical behaviour before escape. Motivated by this perspective, we present recent work on products of mixing Markov chains with holes whose measure vanishes as the dimension grows. We establish quantitative stability results for their quasi-stationary measures, taking a first step towards an ergodic theory of conditioned dynamics in high-dimensional systems. Based on joint work with Matteo Tanzi.