Aging of the Metropolis dynamics on the Random Energy Model

2015/02/16 by Jǐŕı Černý, Černý, Jiří, Tobias Wassmer +1 · 2 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Mathematics #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.1502.04535

openalex publication_date 2015/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the Metropolis dynamics of the simplest mean-field spin glass model, the Random Energy Model. We show that this dynamics exhibits aging by showing that the properly rescaled time change process between the Metropolis dynamics and a suitably chosen `fast' Markov chain converges in distribution to a stable subordinator. The rescaling might depend on the realization of the environment, but we show that its exponential growth rate is deterministic.

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• Free energy fluctuations in SK and related spin glass models: A literature survey
• Dynamical Phase Diagram of the REM under independent spin-flips

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