Publication

A new REM conjecture

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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2008
Conference Papers

Abstract

Official source

Related concepts (20)

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.

Spin glass

In condensed matter physics, a spin glass is a magnetic state characterized by randomness, besides cooperative behavior in freezing of spins at a temperature called 'freezing temperature' Tf. In ferromagnetic solids, component atoms' magnetic spins all align in the same direction. Spin glass when contrasted with a ferromagnet is defined as "disordered" magnetic state in which spins are aligned randomly or without a regular pattern and the couplings too are random.

Beal conjecture

The Beal conjecture is the following conjecture in number theory: If where A, B, C, x, y, and z are positive integers with x, y, z ≥ 3, then A, B, and C have a common prime factor. Equivalently, The equation has no solutions in positive integers and pairwise coprime integers A, B, C if x, y, z ≥ 3. The conjecture was formulated in 1993 by Andrew Beal, a banker and amateur mathematician, while investigating generalizations of Fermat's Last Theorem. Since 1997, Beal has offered a monetary prize for a peer-reviewed proof of this conjecture or a counterexample.

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A new REM conjecture

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