Starts 4 May 2021 11:00
Ends 4 May 2021 12:00
Central European Time
High-dimensional random functionals emerge ubiquitously when modeling the energy landscapes of complex systems, and are typically glassy: exploring them with stochastic dynamics is highly non-trivial due to the abundance of metastable minima that trap the system for very large times. The resulting slow dynamics is dominated by activated processes, in which the system jumps between local minima passing through the saddles (or transition states) connecting them. These jumps can be thought of as instantons of an associated dynamical theory. In simple cases (such as in double-well potentials in 1d), instantons can be constructed using the information on the two energy minima and the barrier between them. In high-dimension, the proliferation of minima renders the problem much more complicated: which other minima does the system reach once it escapes from a particular metastable state? Which are the saddles involved in the associated transition path? In this talk I will focus on random Gaussian functionals in high-dimension, for which these questions can be addressed statistically. I will discuss how to use random matrix theory to gain information on the distribution and reciprocal arrangement of the local minima and saddles, and how to exploit this information to build simple dynamical instantons describing activated jumps between nearby minima in configuration space.