arXiv:1502.04535 Abstract | arXiv Analytics

arXiv:1502.04535 [math.PR]Abstract References Reviews Resources

Aging of the Metropolis dynamics on the Random Energy Model

Published 2015-02-16Version 1

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.

Comments: 37 pages

Categories: math.PR

Keywords: random energy model, metropolis dynamics, rescaled time change process, simplest mean-field spin glass model, exponential growth rate

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