Scaling limits of the Bouchaud and Dean trap model on Parisi's tree in ergodic and aging time scales

2025/05/26 by Luiz Renato Fontes, Adriana Hernandez, Fontes, Luiz Renato +1
Economics, Econometrics and Finance · Physics and Astronomy · #Complex Systems and Time Series Analysis #Complex Network Analysis Techniques #Theoretical and Computational Physics

paper · pdf · doi:10.48550/arxiv.2505.20083

Abstract

We take scaling limits of the Bouchaud and Dean trap model on Parisi's tree in time scales where the dynamics is either ergodic (close to equilibrium) or aging (far from equilibrium). These results follow from a continuity theorem formulated for a certain kind of process on trees, which we call a cascading jump evolution, defined in terms of a collection of jump functions, with a cascading structure given by the tree.

Citations

• Asymptotic behavior of a low temperature non-cascading 2-GREM dynamics at extreme time scales
• Asymptotic behavior and aging of a low temperature cascading 2-GREM dynamics at extreme time scales
• Aging in the GREM-like trap model
• Elementary results on K processes with weights
• Scaling limits and aging for asymmetric trap models on the complete graph and K-processes
• Aging in reversible dynamics of disordered systems. I. Emergence of the arcsine law in Bouchaud's asymmetric trap model on the complete graph
• Convergence of symmetric trap models in the hypercube
• Dynamics of trap models
• Spectral characterization of aging: The REM-like trap model
• Bouchaud’s model exhibits two different aging regimes in dimension one
• Random walks with strongly inhomogeneous rates and singular diffusions: convergence, localization and aging in one dimension

Related

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• Scaling limit and aging for directed trap models
• Biased random walk on critical Galton-Watson trees conditioned to\n survive
• Scaling limits and aging for asymmetric trap models on the complete graph and K-processes
• Critical branching processes with immigration: scaling limits of local extinction sets