Publication

A new REM conjecture

Véronique Gayrard
2008
Conference Papers

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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https://infoscience.epfl.ch/entities/publication/468d6f25-0667-4d00-942a-a938ba7d4bdc

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Véronique Gayrard
2008
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/468d6f25-0667-4d00-942a-a938ba7d4bdc

About this result

Related concepts (10)

Geometrization conjecture

In mathematics, Thurston's geometrization conjecture states that each of certain three-dimensional topological spaces has a unique geometric structure that can be associated with it. It is an analogue of the uniformization theorem for two-dimensional surfaces, which states that every simply connected Riemann surface can be given one of three geometries (Euclidean, spherical, or hyperbolic). In three dimensions, it is not always possible to assign a single geometry to a whole topological space.

Conjecture

In mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. Some conjectures, such as the Riemann hypothesis (still a conjecture) or Fermat's Last Theorem (a conjecture until proven in 1995 by Andrew Wiles), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them. Formal mathematics is based on provable truth.

Pólya conjecture

In number theory, the Pólya conjecture (or Pólya's conjecture) stated that "most" (i.e., 50% or more) of the natural numbers less than any given number have an odd number of prime factors. The conjecture was set forth by the Hungarian mathematician George Pólya in 1919, and proved false in 1958 by C. Brian Haselgrove. Though mathematicians typically refer to this statement as the Pólya conjecture, Pólya never actually conjectured that the statement was true; rather, he showed that the truth of the statement would imply the Riemann hypothesis.

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