Aging in Metropolis dynamics of the REM: a proof
成果类型：
Article
署名作者：
Gayrard, Veronique
署名单位：
Centre National de la Recherche Scientifique (CNRS); Aix-Marseille Universite
刊物名称：
PROBABILITY THEORY AND RELATED FIELDS
ISSN/ISSBN：
0178-8051
DOI：
10.1007/s00440-018-0873-6
发表日期：
2019
页码：
501-551
关键词：
摘要：
We consider Metropolis dynamics of the Random Energy Model. We prove that the classical two-time correlation function that allows one to establish aging converges almost surely to the arcsine law distribution function, as predicted in the physics literature, in the optimal domain of the time-scale and temperature parameters where this result can be expected to hold. To do this we link the two-time correlation function to a certain continuous-time clock process which, after proper rescaling, is proven to converge to a stable subordinator almost surely in the random environment and in the fine J1-topology of Skorohod. This fine topology then enables us to deduce from the arcsine law for stable subordinators the asymptotic behavior of the two-time correlation function that characterizes aging.