Translator Disclaimer
2019 Asymptotic behavior and aging of a low temperature cascading 2-GREM dynamics at extreme time scales
Luiz Renato Fontes, Véronique Gayrard
Electron. J. Probab. 24: 1-50 (2019). DOI: 10.1214/19-EJP395

Abstract

We derive scaling limit results for the Hierarchical Random Hopping Dynamics for the cascading two-level GREM at low temperature at extreme time scales. It is known that in the cascading regime there are two static critical temperatures. We show that there exists a (narrow) set of fine tuning temperatures; when they lie below the static lowest critical temperature, three distinct dynamical phases emerge below the lowest critical temperature, with three different types of limiting dynamics depending on whether the temperature is (well) above or below, or at a fine tuning temperature, all of which are given in terms of K processes. We also derive scaling limit results for temperatures between the lowest and he highest critical ones, as well as aging results for all the limiting processes mentioned above, by taking a second small time limit.

Citation

Download Citation

Luiz Renato Fontes. Véronique Gayrard. "Asymptotic behavior and aging of a low temperature cascading 2-GREM dynamics at extreme time scales." Electron. J. Probab. 24 1 - 50, 2019. https://doi.org/10.1214/19-EJP395

Information

Received: 30 April 2019; Accepted: 15 November 2019; Published: 2019
First available in Project Euclid: 18 December 2019

zbMATH: 07149382
MathSciNet: MR4049078
Digital Object Identifier: 10.1214/19-EJP395

Subjects:
Primary: 60K35, 82C44

JOURNAL ARTICLE
50 PAGES


SHARE
Vol.24 • 2019
Back to Top