Proof of the local REM conjecture for number partitioning I: Constant energy scales

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dc.creatorBorgs, Christian
dc.creatorChayes, Jennifer
dc.creatorMertens, Stephan
dc.creatorNair, Chandra
dc.date2005-01-31
dc.date2005-04-22
dc.date.accessioned2026-07-07T03:03:32Z
dc.date.available2026-07-07T03:03:32Z
dc.descriptionThe number partitioning problem is a classic problem of combinatorial optimization in which a set of $n$ numbers is partitioned into two subsets such that the sum of the numbers in one subset is as close as possible to the sum of the numbers in the other set. When the $n$ numbers are i.i.d. variables drawn from some distribution, the partitioning problem turns out to be equivalent to a mean-field antiferromagnetic Ising spin glass. In the spin glass representation, it is natural to define energies -- corresponding to the costs of the partitions, and overlaps -- corresponding to the correlations between partitions. Although the energy levels of this model are {\em a priori} highly correlated, a surprising recent conjecture asserts that the energy spectrum of number partitioning is locally that of a random energy model (REM): the spacings between nearby energy levels are uncorrelated. In other words, the properly scaled energies converge to a Poisson process. The conjecture also asserts that the corresponding spin configurations are uncorrelated, indicating vanishing overlaps in the spin glass representation. In this paper, we prove these two claims, collectively known as the local REM conjecture.
dc.description26 pages, no figures
dc.identifierhttps://arxiv.org/abs/cond-mat/0501760
dc.identifierhttp://arxiv.org/abs/cond-mat/0501760
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/25785
dc.subjectDisordered Systems and Neural Networks
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.subjectProbability
dc.titleProof of the local REM conjecture for number partitioning I: Constant energy scales
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