The arcsine law as a universal aging scheme for trap models

2006/03/14 by Gérard Ben Arous, Arous, Gerard Ben, Cerny, Jiri · 1 citation
Mathematics · Physics and Astronomy · #60F17 #82C41 #82D30 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.math/0603340

openalex publication_date 2006/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a general proof of aging for trap models using the arcsine law for stable subordinators. This proof is based on abstract conditions on the potential theory of the underlying graph and on the randomness of the trapping landscape. We apply this proof to aging for trap models on large two-dimensional tori and for trap dynamics of the Random Energy Model on a broad range of time scales.

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