Aging of the Metropolis dynamics on the Random Energy Model

Jiří Černý; Tobias Wassmer

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arXiv · 1502.04535

Aging of the Metropolis dynamics on the Random Energy Model

Jiří Černý·Tobias Wassmer

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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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Jiří Černý, Tobias Wassmer. 2015-02-16. Aging of the Metropolis dynamics on the Random Energy Model. https://arxiv.org/abs/1502.04535

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