WIAS Preprint No. 1024, (2005)

A tomography of the GREM: Beyond the REM conjecture


  • Bovier, Anton
  • Kurkova, Irina

2010 Mathematics Subject Classification

  • 60G70 82B45


  • level statistics, random energy model, generalized random energy model, extreme value theory, disordered systems, spin glasses




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. This was proven in a large class of models for energies that do not grow too fast with the system size. Considering the example of the generalized random energy model, we show that the conjecture breaks down for energies proportional to the volume of the system, and describe the far more complex behavior that then sets in.

Appeared in

  • Comm. Math. Phys., 263 (2006) pp. 535-552.

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