A New REM Conjecture

Gérard Ben Arous, Véronique Gayrard, Alexey Kuptsov

Research output: Chapter in Book/Report/Conference proceedingChapter


We introduce here a new universality conjecture for levels of random Hamiltonians, in the same spirit as the local REM conjecture made by S. Mertens and H. Bauke. We establish our conjecture for a wide class of Gaussian and non-Gaussian Hamiltonians, which include the p-spin models, the Sherrington-Kirkpatrick model and the number partitioning problem. We prove that our universality result is optimal for the last two models by showing when this universality breaks down.

Original languageEnglish (US)
Title of host publicationProgress in Probability
Number of pages38
StatePublished - 2008

Publication series

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


  • disordered media
  • spin-glasses
  • Statistical mechanics

ASJC Scopus subject areas

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


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