Aging of the Metropolis dynamics on the random energy model

• 成果类型: Article
• 署名作者: Cerny, Jiri; Wassmer, Tobias
• 署名单位: University of Vienna
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0681-1
• 发表日期: 2017
• 页码: 253-303
• 关键词: random-walk; glauber dynamics; spin-glasses; time; UNIVERSALITY; CONVERGENCE; limit; rem

摘要

We study the Metropolis dynamics of the simplest mean-field spin glass model, the random energy model. We show that this dynamics exhibits aging by showing that the properly rescaled time change process between the Metropolis dynamics and a suitably chosen 'fast' Markov chain converges in distribution to a stable subordinator. The rescaling might depend on the realization of the environment, but we show that its exponential growth rate is deterministic.