- 01-374 G. Ben Arous (EPFL), A. Bovier (WIAS), V. Gayrard (EPFL)
- Glauber Dynamics of the random energy model. 1.
Metastable motion on the extreme states.
Oct 16, 01
(auto. generated ps),
of related papers
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
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.