, Volume 235, Issue 3, pp 379-425

Glauber Dynamics of the Random Energy Model

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Abstract:

 We investigate the long-time behavior of the Glauber dynamics for the random energy model below the critical temperature. We give very precise estimates on the motion of the process to and between the states of extremal energies. We show that when disregarding time, the consecutive steps of the process on these states are governed by a Markov chain that jumps uniformly on all possible states. The mean times of these jumps are also computed very precisely and are seen to be asymptotically independent of the terminal point. A first indicator of aging is the observation that the mean time of arrival in the set of states that have waiting times of order T is itself of order T. The estimates proven in this paper will furnish crucial input for a follow-up paper where aging is analysed in full detail.

Received: 9 October 2001 / Accepted: 17 October 2002 Published online: 28 February 2003
RID="*"
ID="*" Work partially supported by the Swiss National Science Foundation under contract 21-65267.01
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ID="⋆⋆" On leave from CPT-CNRS, Luminy, Case 907, 13288 Marseille Cedex 9, France. E-mail:veronique.gayrard@epfl.ch
Communicated by M. Aizenman