Convergence of symmetric trap models in the hypercube

TL;DR

This paper studies the convergence of symmetric trap models in high-dimensional hypercubes, demonstrating their limit behavior as a K process and applying this to models like REM and RHT dynamics.

Contribution

It establishes the convergence of symmetric trap models to a K process in high dimensions and connects this to the scaling limits of REM-like models and RHT dynamics.

Findings

Models converge to a K process as dimension increases

Application to REM-like trap models

Application to RHT dynamics in the ergodic regime

Abstract

We consider symmetric trap models in the d-dimensional hypercube whose ordered mean waiting times, seen as weights of a measure in the natural numbers, converge to a finite measure as d diverges, and show that the models suitably represented converge to a K process as d diverges. We then apply this result to get K processes as the scaling limits of the REM-like trap model and the Random Hopping Times dynamics for the Random Energy Model in the hypercube in time scales corresponding to the ergodic regime for these dynamics.