Communications in Mathematical Physics

, Volume 263, Issue 2, pp 513–533

Local Energy Statistics in Disordered Systems: A Proof of the Local REM Conjecture


DOI: 10.1007/s00220-005-1516-1

Cite this article as:
Bovier, A. & Kurkova, I. Commun. Math. Phys. (2006) 263: 513. doi:10.1007/s00220-005-1516-1


Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should, in most circumstances, be the same as in the random energy model. Here we give necessary conditions for this hypothesis to be true, which we show to be satisfied in wide classes of examples: short range spin glasses and mean field spin glasses of the SK type. We also show that, under certain conditions, the conjecture holds even if energy levels that grow moderately with the volume of the system are considered.

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  1. 1.Weierstraß–Institut für Angewandte Analysis und StochastikBerlinGermany
  2. 2.Institut für MathematikTechnische Universität BerlinBerlinGermany
  3. 3.Laboratoire de Probabilités et Modèles AléatoiresUniversité Paris 6Paris, Cedex 5France

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