At a microscopic level, spin glasses are strongly disordered, correlated systems that undergo a liquid-to-solid transition without any apparent order emerging. The resulting solids are never observed to be in equilibrium in laboratory experiments; instead, they undergo slow relaxation dynamics instead, with peculiar universal properties that has been termed “aging” in physics.

The aging phenomenon opened a wealth of new problems of probability theory in connection with Markov jump processes in highly disordered random environments. The analysis of several models and dynamics in the past 20 years allowed to isolate a general mechanism that relates aging to the classical arcsine law for stable subordinators through the asymptotic behavior of a partial sum process called clock process. This links aging to some of the most classical parts of probability, namely, extreme value theory, limit theorems for sums of correlated random variables, and Lévy processes.

After a non-technical introduction to spin glasses, I will give an overview of the current knowledge of the aging behavior of mean-field spin glasses (the REM, the p-spin SK models, the GREMs) and explain the key concepts behind the techniques developed to study them.