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143
Universality for orthogonal and symplectic Laguerretype ensembles
 J. Statist. Phys
, 2007
"... Abstract. We give a proof of the Universality Conjecture for orthogonal (β = 1) and symplectic (β = 4) random matrix ensembles of Laguerretype in the bulk of the spectrum as well as at the hard and soft spectral edges. Our results are stated precisely in the Introduction (Theorems 1.1, 1.4, 1.6 and ..."
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Cited by 16 (0 self)
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Abstract. We give a proof of the Universality Conjecture for orthogonal (β = 1) and symplectic (β = 4) random matrix ensembles of Laguerretype in the bulk of the spectrum as well as at the hard and soft spectral edges. Our results are stated precisely in the Introduction (Theorems 1.1, 1.4, 1
On Orthogonal and Symplectic Matrix Ensembles
 MATHEMATICAL PHYSICS
, 1996
"... The focus of this paper is on the probability, Eβ(Q; J), that a set J consisting of a finite union of intervals contains no eigenvalues for the finite N Gaussian Orthogonal (β = 1) and Gaussian Symplectic (β = 4) Ensembles and their respective scaling limits both in the bulk and at the edge of the ..."
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Cited by 259 (10 self)
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The focus of this paper is on the probability, Eβ(Q; J), that a set J consisting of a finite union of intervals contains no eigenvalues for the finite N Gaussian Orthogonal (β = 1) and Gaussian Symplectic (β = 4) Ensembles and their respective scaling limits both in the bulk and at the edge
Symplectic structure of the real Ginibre ensemble
, 2007
"... Abstract. We give a simple derivation of all npoint densities for the eigenvalues of the real Ginibre ensemble with even dimension N as quaternion determinants. A very simple symplectic kernel governs both, the real and complex correlations. 1and2point correlations are discussed in more detail. ..."
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Cited by 13 (0 self)
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Abstract. We give a simple derivation of all npoint densities for the eigenvalues of the real Ginibre ensemble with even dimension N as quaternion determinants. A very simple symplectic kernel governs both, the real and complex correlations. 1and2point correlations are discussed in more detail
Random Matrices of Circular Symplectic Ensemble
"... Abstract: Random unitary matrices of symplectic ensemble describe statistical properties of timedependent, periodical quantum systems with a halfinteger spin. We present amethod of constructing random matrices typical to circular symplectic ensemble and show that the numerically generated unitary ..."
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Cited by 1 (0 self)
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Abstract: Random unitary matrices of symplectic ensemble describe statistical properties of timedependent, periodical quantum systems with a halfinteger spin. We present amethod of constructing random matrices typical to circular symplectic ensemble and show that the numerically generated
Fermion Mapping for Orthogonal and Symplectic Ensembles
"... The circular orthogonal and circular symplectic ensembles are mapped onto free, nonhermitian fermion systems. As an illustration, the twolevel form factors are calculated. ..."
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The circular orthogonal and circular symplectic ensembles are mapped onto free, nonhermitian fermion systems. As an illustration, the twolevel form factors are calculated.
Universality in random matrix theory for orthogonal and symplectic ensembles
, 2004
"... We give a proof of the Universality Conjecture for orthogonal (β = 1) and symplectic (β = 4) ensembles of random matrices in the scaling limit for a class of weights w(x) = e −V (x) where V is a polynomial, V (x) = κ2mx 2m + · · ·, κ2m> 0. For such weights the associated equilibrium measure is ..."
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Cited by 31 (5 self)
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We give a proof of the Universality Conjecture for orthogonal (β = 1) and symplectic (β = 4) ensembles of random matrices in the scaling limit for a class of weights w(x) = e −V (x) where V is a polynomial, V (x) = κ2mx 2m + · · ·, κ2m> 0. For such weights the associated equilibrium measure
Universality at the edge of the spectrum for unitary, orthogonal and symplectic ensembles of random matrices
 Comm. Pure Appl. Math
"... Abstract. We prove universality at the edge of the spectrum for unitary (β = 2), orthogonal (β = 1) and symplectic (β = 4) ensembles of random matrices in the scaling limit for a class of weights w(x) = e −V (x) where V is a polynomial, V (x) = κ2mx 2m + · · · , κ2m> 0. The precise statement ..."
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Cited by 55 (6 self)
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Abstract. We prove universality at the edge of the spectrum for unitary (β = 2), orthogonal (β = 1) and symplectic (β = 4) ensembles of random matrices in the scaling limit for a class of weights w(x) = e −V (x) where V is a polynomial, V (x) = κ2mx 2m + · · · , κ2m> 0. The precise statement
Matrix kernels for the Gaussian orthogonal and symplectic ensembles
 Ann. Inst. Fourier, Grenoble
"... For a large class of finite N determinantal processes the limiting distribution, as N →∞, of the rightmost “particle ” is expressible as the Fredholm determinant of an operator KAiry with kernel A(x)A ′ (y) − A ′ (x)A(y) ..."
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Cited by 17 (2 self)
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For a large class of finite N determinantal processes the limiting distribution, as N →∞, of the rightmost “particle ” is expressible as the Fredholm determinant of an operator KAiry with kernel A(x)A ′ (y) − A ′ (x)A(y)
The Complex Laguerre Symplectic Ensemble of NonHermitian Matrices
, 2005
"... We solve the complex extension of the chiral Gaussian Symplectic Ensemble, defined as a Gaussian twomatrix model of chiral nonHermitian quaternion real matrices. This leads to the appearance of Laguerre polynomials in the complex plane and we prove their orthogonality. Alternatively, a complex eig ..."
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Cited by 8 (2 self)
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We solve the complex extension of the chiral Gaussian Symplectic Ensemble, defined as a Gaussian twomatrix model of chiral nonHermitian quaternion real matrices. This leads to the appearance of Laguerre polynomials in the complex plane and we prove their orthogonality. Alternatively, a complex
CORRELATION KERNELS FOR DISCRETE SYMPLECTIC AND ORTHOGONAL ENSEMBLES
, 712
"... Abstract. In [41] H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials. We obtain similar results for discrete ensembles with rational discrete logarithmic derivative, and compute explicitly correlatio ..."
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Cited by 4 (4 self)
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Abstract. In [41] H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials. We obtain similar results for discrete ensembles with rational discrete logarithmic derivative, and compute explicitly
Results 1  10
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143