Scaling limit and aging for directed trap models

2007/12/12 by Olivier Zindy, Zindy, Olivier
Mathematics · Physics and Astronomy · #60F17 (Primary) #60G52 #60K37 #82D30 (Secondary) #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #math.PR #msc:60F17 #msc:60G52 #msc:60K37 #msc:82D30

paper · pdf · doi:10.48550/arxiv.0712.1951

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

openalex publication_date 2007/12/12 · arxiv created 2008/07/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Universality of the REM for dynamics of mean-field spin glasses
• The arcsine law as a universal aging scheme for trap models
• Limit laws for transient random walks in random environment on \z

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