In this letter we announce rigorous results on the phenomenon of aging in the Glauber dynamics of the random energy model and their relation to Bouchauds REM-like trap model. We show that, below the critical temperature, if we consider a time-scale that diverges with the system size in such a way that equilibrium is almost, but not quite reached on that scale, a suitably defined autocorrelation function has the same asymptotic behaviour than its analog in the trap model.
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