Universality of random Hamiltonians
by Kuptsov, Alexey, Ph.D., NEW YORK UNIVERSITY, 2008, 191 pages; 3320805

Abstract:

We introduce a new REM 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. In addition, we improve the previously known results on Merten's conjecture. In particular, we prove that the local REM universality holds for p-spin models with p larger than 2 for energy scales of the same order as the maximum.
 
AdviserGerard Ben@Arous
SchoolNEW YORK UNIVERSITY
SourceDAI/B 69-08, p. , Nov 2008
Source TypeDissertation
SubjectsMathematics
Publication Number3320805
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