Hamiltonian dynamics of Gaussian random potentials

Speaker. Daniel Peralta-Salas
Date. 25.04.23 at 2:00 pm

Abstract. How is the dynamics of a natural Hamiltonian system (on the cotangent bundle of a compact manifold) for a generic potential? Is it typically nonintegrable or ergodic? In this lecture I will present this problem, which is widely open, and the probabilistic approach that we have developed to shed some light on it. Key to our construction is the concept of Gaussian random potential, which is substantially inspired by the celebrated theory of Nazarov and Sodin in the context of random monochromatic waves. This is based on joint work with A. Enciso and A. Romaniega.