Tony Lelievre

Le 22 sept. 2026 from 02:00PM à 03:30PM

The QSD approach to metastability: from stochastic processes to jump models and shape optimization

Abstract: The aim of this talk is to present an approach that we have developed over the past decade to analyze metastable stochastic processes using quasi-stationary distributions (QSDs). A key advantage of this approach is that it provides a rigorous connection between Markov processes on continuous state spaces and Markov processes on discrete state spaces, whose states index the metastable regions. This work is motivated by questions arising in molecular simulation, particularly the justification of models based on Markov jump processes between states—kinetic Monte Carlo models—and the analysis of related sampling algorithms, such as accelerated dynamics. Finally, I will present recent results from Noé Blassel’s PhD research, in which shape optimization techniques are used to optimize the definition of metastable states.