Scaling Limit and Aging for Directed Trap Models
O. Zindy
2009, v.15, Issue 1, 31-50
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 universality of this phenomenon described by Ben Arous and Cerny for a large class of graphs.
Keywords: directed trap model,random walk,scaling limit,subordinator,aging
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