This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Ben Arous, GérardBovier, AntonČerný, Jiři2016-03-242019-06-2820070946-8633https://doi.org/10.34657/3441https://oa.tib.eu/renate/handle/123456789/1883We consider a version of a Glauber dynamics for a $p$-spin Sherrington--Kirkpatrick model of a spin glass that can be seen as a time change of simple random walk on the $N$-dimensional hypercube. We show that, for any $p geq 3$ and any inverse temperature $beta>0$, there exist constants $g_0>0$, such that for all exponential time scales, $exp(gamma N)$, with $gleq g_0$, the properly rescaled emphclock process (time-change process), converges to an $a$-stable subordinator where $a=g/b^2<1$. Moreover, the dynamics exhibits aging at these time scales with time-time correlation function converging to the arcsine law of this hbox$alpha$-stable subordinator. In other words, up to rescaling, on these time scales (that are shorter than the equilibration time of the system), the dynamics of $p$-spin models ages in the same way as the REM, and by extension Bouchaud's REM-like trap model, confirming the latter as a universal aging mechanism for a wide range of systems. The SK model (the case $p=2$) seems to belong to a different universality class.application/pdfeng510Report