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

Gérard Ben Arous, Anton Bovier, Véronique Gayrard

Research output: Contribution to journalArticle


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 auto-correlation 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.

Original languageEnglish (US)
Pages (from-to)1-54
Number of pages54
JournalCommunications In Mathematical Physics
Issue number1
StatePublished - May 1 2003


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this