Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles
نویسنده
چکیده
In [41] H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polyno-mials. We obtain similar results for discrete ensembles with rational discrete logarithmic derivative, and compute explicitly correlation kernels associated to the classical Meixner and Charlier weights.
منابع مشابه
Correlation Functions, Cluster Functions, and Spacing Distributions for Random Matrices
The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm determinants of matrix-valued kernels. The derivations of the various formulas are somewhat involved. In this article we present a direct approach which leads immediate...
متن کاملOn Orthogonal and Symplectic Matrix Ensembles Associated with a Class of Weight Functions
For the unitary ensembles of N × N Hermitian matrices associated with a weight function w there is a kernel, expressible in terms of the polynomials orthogonal with respect to the weight function, which plays an important role. For example the n-point correlation function and the spacing probabilities have nice representations in terms of this kernel. For the orthogonal and symplectic ensembles...
متن کاملAverages of Characteristic Polynomials in Random Matrix Theory
We compute averages of products and ratios of characteristic polynomials associated with Orthogonal, Unitary, and Symplectic Ensembles of Random Matrix Theory. The pfaffian/determinantal formulas for these averages are obtained, and the bulk scaling asymptotic limits are found for ensembles with Gaussian weights. Classical results for the correlation functions of the random matrix ensembles and...
متن کاملUniversality at the Edge of the Spectrum for Unitary, Orthogonal and Symplectic Ensembles of Random Matrices
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 (x) where V is a polynomial, V (x) = κ2mx + · · · , κ2m > 0. The precise statement of our results is given in Theorem 1.1 and Corollaries 1.2, 1.3 below. For a proof of universality in the bul...
متن کاملUniversality for Orthogonal and Symplectic Laguerre-type Ensembles
We give a proof of the Universality Conjecture for orthogonal (β = 1) and symplectic (β = 4) random matrix ensembles of Laguerre-type in the bulk of the spectrum as well as at the hard and soft spectral edges. They concern the appropriately rescaled kernels K n,β , correlation and cluster functions, gap probabilities and the distributions of the largest and smallest eigenvalues. Corresponding r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008