EVENT DETAILS AND ABSTRACT

Title: Kawasaki dynamics beyond the uniqueness threshold
Speaker: Benoit Dagallier
Speaker Info: New York University
Brief Description: Kawasaki dynamics beyond the uniqueness threshold
Special Note:
Abstract:

Consider the problem of sampling from a prototypical statistical mechanics model, the Ising model on a finite graph. This problem has been extensively studied, with for instance mixing time bounds known for a popular class of (Markov chain Monte Carlo) samplers, the so-called Glauber dynamics. The typical picture for such dynamics is that the mixing time is related to the physics of the model: mixing is fast when there is no phase transition and drastically slows down when there is one.

In this talk, I will discuss the Ising model conditioned to have fixed magnetisation and the natural analogue of Glauber dynamics in that setting, the so-called Kawasaki dynamics. I will show that, on many graphs, the Kawasaki dynamics remarkably remains fast beyond the phase transition threshold. This indicates that, on such graphs, the magnetisation is the only observable causing the slowdown of Glauber dynamics at the transition.

The proof uses the Polchinski flow decomposition of a measure (also known as stochastic localisation) and the so-called entropic stability to reduce to estimates on infinite-temperature Ising measures with fixed magnetisation. Such measures are studied using the down-up walk formalism of Anari et al. I will try to provide a pedagogical introduction to these techniques.

The talk is based on the joint work https://arxiv.org/abs/2310.04609 with Roland Bauerschmidt and Thierry Bodineau.