Abstract
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.
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Arous, G.B., Gayrard, V., Kuptsov, A. (2008). A New REM Conjecture. In: Sidoravicius, V., Vares, M.E. (eds) In and Out of Equilibrium 2. Progress in Probability, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8786-0_4
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DOI: https://doi.org/10.1007/978-3-7643-8786-0_4
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