The arcsine law as a universal aging scheme for trap models
Gerard Ben Arous, Jiri Cerny
TL;DR
This paper provides a universal aging framework for trap models using the arcsine law, applicable to various models and graph structures, advancing understanding of aging phenomena in disordered systems.
Contribution
It introduces a general proof of aging for trap models based on potential theory and the arcsine law, extending to large tori and the Random Energy Model.
Findings
Aging behavior is proven for trap models on large 2D tori.
The proof applies to trap dynamics of the Random Energy Model across multiple time scales.
The approach relies on abstract potential theory and landscape randomness.
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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Taxonomy
TopicsStochastic processes and statistical mechanics · Theoretical and Computational Physics · Markov Chains and Monte Carlo Methods