Aging of the Metropolis dynamics on the Random Energy Model
Probability
2015-02-17 v1
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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Cite
@article{arxiv.1502.04535,
title = {Aging of the Metropolis dynamics on the Random Energy Model},
author = {Jiří Černý and Tobias Wassmer},
journal= {arXiv preprint arXiv:1502.04535},
year = {2015}
}
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37 pages