Extremal aging for trap models

Abstract

In the seminal work [5], Ben Arous and Cerný give a general characterization of aging for trap models in terms of α-stable subordinators with α ∈ (0,1). Some of the important examples that fall into this universality class are Random Hopping Time (RHT) dynamics of Random Energy Model (REM) and p-spin models observed on exponential time scales. In this paper, we explain a different aging mechanism in terms of extremal processes that can be seen as the extension of α-stable aging to the case α=0. We apply this mechanism to the RHT dynamics of the REM for a wide range of temperature and time scales. The other examples that exhibit extremal aging include the Sherrington Kirkpatrick (SK) model and p-spin models [6, 9], and biased random walk on critical Galton-Watson trees conditioned to survive [11].