Cugliandolo-Kurchan equations for dynamics of spin-glasses

Gérard Ben Arous, Amir Dembo, Alice Guionnet

Research output: Contribution to journalArticlepeer-review


We study the Langevin dynamics for the family of spherical p-spin disordered mean-field models of statistical physics. We prove that in the limit of system size N approaching infinity, the empirical state correlation and integrated response functions for these N-dimensional coupled diffusions converge almost surely and uniformly in time, to the non-random unique strong solution of a pair of explicit non-linear integro-differential equations intensively studied by Cugliandolo and Kurchan.

Original languageEnglish (US)
Pages (from-to)619-660
Number of pages42
JournalProbability Theory and Related Fields
Issue number4
StatePublished - Dec 2006


  • Aging
  • Disordered systems
  • Interacting random processes
  • Langevin dynamics
  • Statistical mechanics
  • p-spin models

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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