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

TL;DR

This paper investigates the scaling limits of the Bouchaud and Dean trap model on Parisi's tree, revealing behavior in both ergodic and aging regimes through a new continuity theorem for cascading jump processes.

Contribution

It introduces a continuity theorem for cascading jump evolutions on trees, enabling analysis of the trap model's scaling limits in different dynamical regimes.

Findings

Derived scaling limits in ergodic and aging time scales

Established a new continuity theorem for cascading jump processes

Provided insights into the trap model's long-term behavior

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.