Scaling limit and aging for directed trap models

Abstract

We consider one-dimensional directed trap models and suppose that the trapping times are heavy-tailed. We obtain the inverse of a stable subordinator as scaling limit and prove an aging phenomenon expressed in terms of the generalized arcsine law. These results confirm the status of universality described by Ben Arous and Černý for a large class of graphs.

16 pages, accepted for publication in "Markov processes and Related Fields"

References in corpus (6)

• Scaling limit for trap models on ${\mathbb{Z}}^d$
• Non-linear Response of the trap model in the aging regime : Exact results in the strong disorder limit
• Linear and non linear response in the aging regime of the 1D trap model
• Limit laws for transient random walks in random environment on $\z$
• The arcsine law as a universal aging scheme for trap models
• Universality of the REM for dynamics of mean-field spin glasses