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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
Biorthogonal ensembles
 Nuclear Phys. B
, 1999
"... Abstract. One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one–parametric deformation of these ensembles, which is defined in terms of the biorthogonal po ..."
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Cited by 12 (2 self)
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polynomials of Jacobi, Laguerre and Hermite type. Our main result is a series of explicit expressions for the correlation functions in the scaling limit (as the number of points goes to infinity). As in the classical case, the correlation functions have determinantal form. They are given by certain new
Fredholm Determinants, Differential Equations and Matrix Models
 COMMUNICATIONS IN MATHEMATICAL PHYSICS
, 1994
"... Orthogonal polynomial random matrix models of N x N hermitian matrices lead to Fredholm determinants of integral operators with kernel of the form (φ(x)φ(y) — ψ(x)φ(y))/x — y. This paper is concerned with the Fredholm determinants of integral operators having kernel of this form and where the und ..."
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Cited by 142 (20 self)
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as φ and φ satisfy a certain type of differentiation formula. The (φ, φ) pairs for the sine, Airy, and Bessel kernels satisfy such relations, as do the pairs which arise in the finite N Hermite, Laguerre and Jacobi ensembles and in matrix models of 2D quantum gravity. Therefore we shall be able
Hermite and Laguerre βensembles: asymptotic corrections to the eigenvalue density
"... We consider Hermite and Laguerre βensembles of large N × N random matrices. For all β even, corrections to the limiting global density are obtained, and the limiting density at the soft edge is evaluated. We use the saddle point method on multidimensional integral representations of the density whi ..."
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Cited by 21 (11 self)
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We consider Hermite and Laguerre βensembles of large N × N random matrices. For all β even, corrections to the limiting global density are obtained, and the limiting density at the soft edge is evaluated. We use the saddle point method on multidimensional integral representations of the density
Nonstandard symmetry classes in mesoscopic normalsuperconducting hybrid structures,” arXiv:condmat/9602137 ; Phys
 Rev. B
, 1997
"... Normalconducting mesoscopic systems in contact with a superconductor are classified by the symmetry operations of time reversal and rotation of the electron's spin. Four symmetry classes are identified, which correspond to Cartan's symmetric spaces of type C, CI, D, and DIII. A detailed ..."
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Cited by 82 (3 self)
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. The remaining two classes are related to the Laguerre orthogonal and symplectic randommatrix ensembles. For a quantum dot with a normalmetalsuperconducting geometry, the weaklocalization correction to the conductance is calculated as a function of sticking probability and two perturbations breaking time
Edgeworth expansion of the largest eigenvalue distribution function of GUE and LUE
, 2006
"... We derive expansions of the Hermite and Laguerre kernels at the edge of the spectrum of the finite n Gaussian Unitary Ensemble (GUEn) and the finite n Laguerre Unitary Ensemble (LUEn), respectively. Using these large n kernel expansions, we prove an Edgeworth type theorem for the largest eigenvalue ..."
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Cited by 12 (2 self)
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We derive expansions of the Hermite and Laguerre kernels at the edge of the spectrum of the finite n Gaussian Unitary Ensemble (GUEn) and the finite n Laguerre Unitary Ensemble (LUEn), respectively. Using these large n kernel expansions, we prove an Edgeworth type theorem for the largest eigenvalue
Orbit measures, random matrix theory and interlaced determinantal processes
, 2009
"... A connection between representation of compact groups and some invariant ensembles of Hermitian matrices is described. We focus on two types of invariant ensembles which extend the Gaussian and the Laguerre Unitary ensembles. We study them using projections and convolutions of invariant probability ..."
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Cited by 13 (0 self)
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A connection between representation of compact groups and some invariant ensembles of Hermitian matrices is described. We focus on two types of invariant ensembles which extend the Gaussian and the Laguerre Unitary ensembles. We study them using projections and convolutions of invariant
Average Characteristic Polynomials of Determinantal Point Processes
, 2013
"... We investigate the average characteristic polynomial E [ ∏N i=1 (z −xi) ] where the xi’s are real random variables drawn from a Biorthogonal Ensemble, i.e. a determinantal point process associated with a bounded finiterank projection operator. For a subclass of Biorthogonal Ensembles, which contain ..."
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Cited by 5 (0 self)
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contains Orthogonal Polynomial Ensembles and (mixedtype) Multiple Orthogonal Polynomial Ensembles, we provide a sufficient condition for its limiting zero distribution to match with the limiting distribution of the random variables, almost surely, as N goes to infinity. Moreover, such a condition turns
On Certain Wronskians of Multiple Orthogonal Polynomials
"... Abstract. We consider determinants of Wronskian type whose entries are multiple orthogonal polynomials associated with a path connecting two multiindices. By assuming that the weight functions form an algebraic Chebyshev (AT) system, we show that the polynomials represented by the Wronskians keep ..."
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Cited by 1 (0 self)
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– the AT ensemble. As the second application, we derive some Turán type inequalities for multiple Hermite and multiple Laguerre polynomials (of two kinds). Finally, we study numerically the geometric configuration of zeros for the Wronskians of these multiple orthogonal polynomials. We observe that the zeros have
Asymptotic behavior of random determinants
 in the Laguerre, Gram and Jacobi ensembles, arXiv math.PR/0607767
, 2007
"... Abstract. We consider properties of determinants of some random symmetric matrices issued from multivariate statistics: Wishart/Laguerre ensemble (sample covariance matrices), Uniform Gram ensemble (sample correlation matrices) and Jacobi ensemble (MANOVA). If n is the size of the sample, r ≤ n the ..."
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Cited by 8 (4 self)
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Abstract. We consider properties of determinants of some random symmetric matrices issued from multivariate statistics: Wishart/Laguerre ensemble (sample covariance matrices), Uniform Gram ensemble (sample correlation matrices) and Jacobi ensemble (MANOVA). If n is the size of the sample, r ≤ n
Results 1  10
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