Aging of the Metropolis dynamics on the random energy model. (English) Zbl 1359.82018
Summary: 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.
MSC:
| 82C44 | Dynamics of disordered systems (random Ising systems, etc.) in time-dependent statistical mechanics |
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
| 60K37 | Processes in random environments |
| 82C80 | Numerical methods of time-dependent statistical mechanics (MSC2010) |
| 65C40 | Numerical analysis or methods applied to Markov chains |
| 60J22 | Computational methods in Markov chains |
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