REM Universality for Random Hamiltonians

Gérard Ben Arous, Alexey Kuptsov

Research output: Chapter in Book/Report/Conference proceedingChapter


We survey in this paper a universality phenomenon which shows that some characteristics of complex random energy landscapes are model-independent, or universal. This universality, called REM-universality, was discovered by S. Mertens and H. Bauke in the context of combinatorial optimization. We survey recent advances on the extent of this REM-universality for equilibrium as well as dynamical properties of spin glasses. We also focus on the limits of REM-universality, i.e., when it ceases to be valid.

Original languageEnglish (US)
Title of host publicationProgress in Probability
Number of pages40
StatePublished - 2009

Publication series

NameProgress in Probability
ISSN (Print)1050-6977
ISSN (Electronic)2297-0428


  • Gaussian processes
  • Spin glasses
  • disordered media
  • extreme values
  • random energy model
  • statistical mechanics

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics (miscellaneous)
  • Mathematical Physics
  • Applied Mathematics


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