Communications in Mathematical Physics

, Volume 263, Issue 2, pp 513–533

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


    • Weierstraß–Institut für Angewandte Analysis und Stochastik
    • Institut für MathematikTechnische Universität Berlin
  • Irina Kurkova
    • Laboratoire de Probabilités et Modèles AléatoiresUniversité Paris 6

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.

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© Springer-Verlag Berlin Heidelberg 2006