99 research outputs found
Asymptotics for the Fredholm Determinant of the Sine Kernel on a Union of Intervals
In the bulk scaling limit of the Gaussian Unitary Ensemble of Hermitian
matrices the probability that an interval of length contains no eigenvalues
is the Fredholm determinant of the sine kernel over
this interval. A formal asymptotic expansion for the determinant as tends
to infinity was obtained by Dyson. In this paper we replace a single interval
of length by where is a union of intervals and present a proof
of the asymptotics up to second order. The logarithmic derivative with respect
to of the determinant equals a constant (expressible in terms of
hyperelliptic integrals) times , plus a bounded oscillatory function of
(zero of , periodic if , and in general expressible in terms of the
solution of a Jacobi inversion problem), plus . Also determined are the
asymptotics of the trace of the resolvent operator, which is the ratio in the
same model of the probability that the set contains exactly one eigenvalue to
the probability that it contains none. The proofs use ideas from orthogonal
polynomial theory.Comment: 24 page
Organic Superconductors: when correlations and magnetism walk in
This survey provides a brief account for the start of organic
superconductivity motivated by the quest for high Tc superconductors and its
development since the eighties'. Besides superconductivity found in 1D organics
in 1980, progresses in this field of research have contributed to better
understand the physics of low dimensional conductors highlighted by the wealth
of new remarkable properties. Correlations conspire to govern the low
temperature properties of the metallic phase. The contribution of
antiferromagnetic fluctuations to the interchain Cooper pairing proposed by the
theory is borne out by experimental investigations and supports
supercondutivity emerging from a non Fermi liquid background. Quasi one
dimensional organic superconductors can therefore be considered as simple
prototype systems for the more complex high Tc materials.Comment: 41 pages, 21 figures to be published in Journal of Superconductivity
and Novel Magnetis
Effects on profits and risks of hedging hogs in the futures market
Swine Day '76 is known as Swine Day, 1976Erratic hog prices in recent years have compounded management problems. As a result, interest has increased in ways of tying down prices before the hogs are ready for market. This report presents results of a study of one approach to the problem -- hedging in the futures market
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