Banach Lie-Poisson Spaces and Reduction

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