Probability Theory and Related Fields

, Volume 157, Issue 1, pp 251–283

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

Article

DOI: 10.1007/s00440-012-0456-x

Cite this article as:
Bovier, A., Gayrard, V. & Švejda, A. Probab. Theory Relat. Fields (2013) 157: 251. doi:10.1007/s00440-012-0456-x

Abstract

This paper extends recent results on ageing in mean field spin glasses on short time scales, obtained by Ben Arous and Gün (Commun Pure Appl Math 65:77–127, 2012) 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 in Aging in reversible dynamics of disordered systems. II. Emergence of the arcsine law in the random hopping time dynamics of the REM, 2010; Electron J Probab 17(58): 1–33, 2012) and naturally complements (Bovier and Gayrard in Ann Probab, 2012).

Keywords

Ageing Spin glasses Random environments Clock process  Lévy processes Extremal processes 

Mathematics Subject Classification (2000)

82C44 60K35 60G70 

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Anton Bovier
    • 1
  • Véronique Gayrard
    • 2
  • Adéla Švejda
    • 1
  1. 1.Institut für Angewandte MathematikRheinische Friedrich-Wilhelms-UniversitätBonnGermany
  2. 2.CMI, LAPTUniversité de ProvenceMarseille Cedex 13France