Statistical properties of barriers and activated dynamics in mean-field models of glasses

Understanding the geometrical properties of high-dimensional, random energy landscapes is a central problem in the physics of glassy systems, as well as in interdisciplinary applications to computer science, ecology and biology.
In this talk I will discuss a framework to compute the statistical distribution of stationary points of random landscapes, making use of a replicated version of the Kac-Rice formula. I will focus on models which provide a mean-field description of the glass transition, and discuss how to compute the statistics of the energy barriers between local minima of the landscape. I will discuss the dynamical implications on these results, especially for the activated regime of the dynamics.