| In this work we study dynamics of mean-field spin-glasses. Our main result is that the global behavior of the dynamics of Sherrington-Kirkpatrick (SK) model is not effected by the correlations for very long time scales, namely, exp(o(n)) where n is the volume of the system. This, for the first time, extends the universality of the Random Energy Model (REM) to the dynamics of the SK model.;In order to first understand the behavior of REM dynamics in subexponential times, we start working with a general viewpoint of Bouchaud's trap model on graphs. We give a common mechanism explaining the two-time correlation properties of trap models under certain potential theoretical conditions for the underlying graph and randomness of the trapping landscape. In these regimes, extremal processes emerge as a universal tool to explain behaviors of clock processes. Moreover, trap models have decorrelation properties similar to aging, which we call extremal aging. Finally, using this method we show that in subexponential times, the clock process of REM non-linearly normalized converges to an extremal process and that the dynamics of the REM model ages extremely.;Next, we investigate the dynamics of SK and p-spin models. For any of these models, we prove that the non-linearly normalized clock process converges to an extremal process on any subexponential time scale. Moreover, the dynamics ages extremely in the same way as REM. Hence, by extension, this confirms Bouchaud's REM-like trap model as a universal aging mechanism for a wide range of systems which, for the first time, includes the SK model. |
