WIAS Preprint No. 691, (2001)

Glauber dynamics of the random energy model II. Aging below the critical temperature



Authors

  • Ben Arous, Gérard
  • Bovier, Anton
  • Gayrard, Véronique

2010 Mathematics Subject Classification

  • 82C44 60K35

Keywords

  • aging, Glauber dynamics, random energy model, trap models, metastability, extreme values

Abstract

We investigate the long-time behavior of the Glauber dynamics for the random energy model below the critical temperature. We establish that for a suitably chosen timescale that diverges with the size of the system, one can prove that a natural autocorrelation function exhibits aging. Moreover, we show that the long-time asymptotics of this function coincide with those of the so-called "REM-like trap model" proposed by Bouchaud and Dean. Our results rely on very precise estimates on the distribution of transition times of the process between different states of extremely low energy.

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