Convergence to extremal processes in random environments and extremal ageing in SK models

TL;DR

This paper investigates the convergence behavior of extremal processes in random environments and explores extremal aging phenomena in SK models, extending prior results to hold almost surely and in probability.

Contribution

It advances the understanding of aging in mean field spin glasses by establishing almost sure and probabilistic convergence results using methods from Gayrard, complementing earlier work by Bovier and Gayrard.

Findings

Convergence to extremal processes in random environments.

Almost sure and in probability aging results in SK models.

Extension of prior law-based results to stronger modes of convergence.

Abstract

This paper extends recent results on aging in mean field spin glasses on short time scales, obtained by Ben Arous and Gun [2] in law with respect to the environment, to results that hold almost surely, respectively in probability, with respect to the environment. It is based on the methods put forward in Gayrard [8,9] and naturally complements Bovier and Gayrard [6].