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We study the aging behavior of the Random Energy Model (REM) evolving underMetropolis dynamics. We prove that a classical two-time correlation functionconverges almost surely to the arcsine law distribution function thatcharacterizes activated aging, as predicted in the physics literature, in theoptimal domain of the time-scale and temperature parameters where this resultcan be expected to hold. In the course of the proof we establish that a certaincontinuous time clock process, after proper rescaling, converges almost surelyto a stable subordinator, improving upon the result of Cerny and Wassmer (2015)where a closely related clock is shown to converge in probability only, and ina restricted region of the time-scale and temperature parameters. The randomrescaling involved in this convergence is controlled at the fine level offluctuations. As a byproduct, we refine and prove a conjecture made in Cernyand Wassmer (2015).

Aging in Metropolis dynamics of the REM: a proof