77Bal1 - 83Rey1

Forrester, A. R.

doi:10.1007/10834579_97

Cited by 5 publications

(6 citation statements)

References 716 publications

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“…This universality has since been derived by other authors [24,25,26] using alternative methods, and verified numerically [21]. It is perhaps useful to remark here that, while there are notable exceptions of course, much of the literature on random matrix theory, as far as we know, is devoted to the Gaussian case [12,13].…”

Section: Introductionsupporting

confidence: 57%

Universal relation between Green functions in random matrix theory

Zee

Brézin

1995

Nuclear Physics B

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We prove that in random matrix theory there exists a universal relation between the one-point Green's function G and the connected two-point Green's function G c given byThis relation is universal in the sense that it does not depend on the probability distribution of the random matrices for a broad class of distributions, even though G is known to depend on the probability distribution in detail. The universality discussed here represents a different statement than the universality we discovered a couple of 1 years ago, which states that a 2 G c (az, aw) is independent of the probability distribution, where a denotes the width of the spectrum and depends sensitively on the probability distribution. It is shown that the universality proved here also holds for the more general problem of a Hamiltonian consisting of the sum of a deterministic term and a random term analyzed perturbatively

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Section: Introductionsupporting

confidence: 57%

Universal relation between Green functions in random matrix theory

Zee

Brézin

1995

Nuclear Physics B

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“…This result could be derived by other methods, and indeed has been obtained in a somewhat different form by Ambjorn and Makeenko and others [11]. The derivation given here however gives the correlation function even for finite N. One can check easily that the derivation that we have given here through Kazakov's representation, could be repeated for calculating the two-point correlation function in the unitary ensemble, in which the universality of the two-point correlation function has been studied [12,13,14,15,16,17,18]. It is not difficult to verify that the above expression for the connected two-point correlation is a compact version of the one that we would have deduced from the orthogonal polynomial method, with the kernel K(λ 1 , λ 2 ) in (2.8).…”

Section: (346)mentioning

confidence: 74%

Oscillating density of states near zero energy for matrices made of blocks with possible application to the random flux problem

1996

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We consider random hermitian matrices made of complex blocks. The symmetries of these matrices force them to have pairs of opposite real eigenvalues, so that the average density of eigenvalues must vanish at the origin. These densities are studied for finite N × N matrices in the Gaussian ensemble. In the large N limit the density of eigenvalues is given by a semi-circle law. However, near the origin there is a region of size 1 N in which this density rises from zero to the semi-circle, going through an oscillatory behavior. This cross-over is calculated explicitly by various techniques. We then show to first order in the non-Gaussian character of the probability distribution that this oscillatory behavior is universal, i.e. independent of the probability distribution. We conjecture that this universality holds to all orders. We then extend our consideration to the more complicated block matrices which arise from lattices of matrices considered in our

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“…The scalar version of the H SCSM (n = 1) has been studied over the course of the past 25 years starting with the work of Sutherland [21]. Among the recent advances one can point out the connection of the H SCSM (n = 1) with Random Matrix Theory [8], exact computation of the dynamical correlation functions [10,11,15] and the intriguing connection with the Virasoro and the W -algebras [2]. To a large extent many of these developments, in particular the computation of the correlation functions, were based on the properties of the symmetric Jack polynomials which describe the orthogonal eigenbasis of the scalar Calogero-Sutherland Model [20,14].…”

Section: Introductionmentioning

confidence: 99%