Probability Theory and Related Fields

, Volume 106, Issue 2, pp 187–232

Sanov results for Glauber spin-glass dynamics

  • M. Grunwald

DOI: 10.1007/s004400050062

Cite this article as:
Grunwald, M. Probab Theory Relat Fields (1996) 106: 187. doi:10.1007/s004400050062


In this paper we prove a Sanov result, i.e. a Large Deviation Principle (LDP) for the distribution of the empirical measure, for the annealed Glauber dynamics of the Sherrington-Kirkpatrick spin-glass. Without restrictions on time or temperature we prove a full LDP for the asymmetric dynamics and the crucial upper large deviations bound for the symmetric dynamics. In the symmetric model a new order-parameter arises corresponding to the response function in [SoZi83]. In the asymmetric case we show that the corresponding rate function has a unique minimum, given as the solution of a self-consistent equation. The key argument used in the proofs is a general result for mixing of what is known as Large Deviation Systems (LDS) with measures obeying an independent LDP.

Mathematics Subject Classification (1991): 60F10, 60H10, 60K35, 82C22, 82C31, 82C44

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • M. Grunwald
    • 1
  1. 1.Fachbereich Mathematik, Technische Universität Berlin, D-10623 Berlin (e-mail: