Ricerc@Sapienza

We would like to study several out of equilibrium dynamics in different disordered models, having an energy landscape of increasing complexity. These out of equilibrium processes are very hard to deal with due to the fact that they do not necessarily follow a Gibbs-like distribution.
We plan to study the performance of simulated annealing in the search for the ground state in the Sherrington-Kirkpatrick model. This is a prototypical disordered model and the question about whether an algorithm scaling linearly in the system size can achieve the optimal configuration is still largely open. The main limitation comes from finite size and finite times effects, that we plan to deal efficiently thank to a new set of large scale numerical simulations and a new analysis taking into account both effects.
The spherical mixed p-spin model is the most used mean-field model for the glass transition. Recently we have uncovered new features in the relaxation dynamics which do not get stuck exactly at the threshold energy, but can go below it. These new findings call for an analytical explanation that we will try to provide by studying a quasi-equilibrium process that should imitate the very slow annealing process.
We also plan to study planted models that play a central role in Bayesian statistical inference. In particular, we will focus on random constraint satisfaction problems with an added solution (the signal). Finding the signal is known to be a very hard problem in a range of the signal-to-noise ratio. Optimal algorithms exist based on Belief Propagation and we plan to study more robust algorithms based on Monte Carlo methods. We are interested in uncovering the algorithmic threshold for the Simulated Annealing algorithm and some variants of it, by the analytical estimation of spinodal and dynamical phase transitions.