Universality and extremal aging for dynamics of spin glasses on subexponential time scales

We consider random hopping time (RHT) dynamics of the Sherrington-Kirkpatrick (SK) model and p-spin models of spin glasses. For any of these models and for any inverse temperature β > 0 we prove that, on time scales that are subexponential in the dimension, the properly scaled clock process (time-change process) of the dynamics converges to an extremal process. Moreover, on these time scales, the system exhibits aging-like behavior, which we call extremal aging. In other words, the dynamics of these models ages as the random energy model (REM) does. Hence, by extension, this confirms Bouchaud's REM-like trap model as a universal aging mechanism for a wide range of systems that, for the first time, includes the SK model.