Aging of asymmetric dynamics on the random energy model

TL;DR

This paper demonstrates aging phenomena in Glauber dynamics on the random energy model by deriving the scaling limits of the clock and age processes, both expressed through stable subordinators, revealing long-term memory effects.

Contribution

It introduces the first rigorous analysis of aging in the random energy model's dynamics, providing explicit stable subordinator limits for key processes.

Findings

Scaling limits of the clock process are established.

The age process limit is characterized by a stable subordinator.

Results confirm aging behavior in the model.

Abstract

We show aging of Glauber-type dynamics on the random energy model, in the sense that we obtain the scaling limits of the clock process and of the age process. The latter encodes the Gibbs weight of the configuration occupied by the dynamics. Both limits are expressed in terms of stable subordinators.