# Dynamic phase diagram of the REM

## TL;DR

This paper provides a detailed analysis of the phase diagram of the REM's dynamics on exponential time scales, using advanced probabilistic methods related to the clock process and random walks.

## Contribution

It introduces a comprehensive approach to understanding the phase diagram of the REM's dynamics through convergence analysis of the clock process and properties of random walks in high dimensions.

## Key findings

- Characterization of phase transitions in the REM dynamics
- Analysis of the clock process convergence properties
- Insights into the behavior of simple random walks in high-dimensional cubes

## Abstract

By studying the two-time overlap correlation function, we give a comprehensive analysis of the phase diagram of the Random Hopping Dynamics of the Random Energy Model (REM) on time-scales that are exponential in the volume. These results are derived from the convergence properties of the clock process associated to the dynamics and fine properties of the simple random walk in the $n$-dimensional discrete cube.