Aging of the Metropolis dynamics on the Random Energy Model
Ji\v{r}\'i \v{C}ern\'y, Tobias Wassmer
TL;DR
This paper investigates aging phenomena in the Metropolis dynamics of the Random Energy Model, demonstrating convergence to a stable subordinator and establishing the deterministic nature of the exponential growth rate of the rescaling.
Contribution
It introduces a novel analysis of aging in the Random Energy Model's Metropolis dynamics, showing convergence to a stable subordinator and the deterministic exponential growth rate.
Findings
Metropolis dynamics exhibits aging behavior.
Rescaled time process converges to a stable subordinator.
Exponential growth rate of rescaling is deterministic.
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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Taxonomy
TopicsTheoretical and Computational Physics · Stochastic processes and statistical mechanics · Complex Systems and Time Series Analysis