A new REM conjecture

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.

34 pages

References in corpus (2)

• Random Costs in Combinatorial Optimization
• Universality in the level statistics of disordered systems

Cited by in corpus (1)

• Local Energy Statistics in Directed Polymers