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

Luiz Renato Fontes; Andrea Hernández

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arXiv · 2505.20083

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

Luiz Renato Fontes·Andrea Hernández

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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.

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Luiz Renato Fontes, Andrea Hernández. 2025-05-26. Scaling limits of the Bouchaud and Dean trap model on Parisi's tree in ergodic and aging time scales. https://arxiv.org/abs/2505.20083

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