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Article Dans Une Revue Probability Theory and Related Fields Année : 2019

Aging in Metropolis dynamics of the REM: a proof

Résumé

We study the aging behavior of the Random Energy Model (REM) evolving under Metropolis dynamics. We prove that a classical two-time correlation function converges almost surely to the arcsine law distribution function that characterizes activated aging, as predicted in the physics literature, in the optimal domain of the time-scale and temperature parameters where this result can be expected to hold. In the course of the proof we establish that a certain continuous time clock process, after proper rescaling, converges almost surely to 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 in a restricted region of the time-scale and temperature parameters. The random rescaling involved in this convergence is controlled at the fine level of fluctuations. As a byproduct, we refine and prove a conjecture made in Cerny and Wassmer (2015).
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Dates et versions

hal-01277223 , version 1 (01-12-2020)

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Véronique Gayrard. Aging in Metropolis dynamics of the REM: a proof. Probability Theory and Related Fields, 2019, 174, pp.501-551. ⟨10.1007/s00440-018-0873-6⟩. ⟨hal-01277223⟩
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