Eigenvalue correlations in non-Hermitean symplectic random matrices
نویسنده
چکیده
Cβ(N) is a normalisation constant, w (z, z̄) is a weight function (see discussion below). For real matrices (β = 1) with no further symmetries, the reader is referred to much later papers by Lehmann and Sommers (1991), and also by Edelman (1997). Although Ginibre’s derivation of Eqs. (1) and (2) holds for random matrices with Gaussian distributed entries, that is for w(z, z̄) = w 0(z, z̄) = e , (3)
منابع مشابه
Eigenvalue Correlations in Ginibre's Non-hermitean Random Matrices at Β = 4
Correlation function of complex eigenvalues of N × N random matrices drawn from Ginibre's non-Hermitean ensemble of symplectic symmetry is given in terms of a quaternion determinant. Spectral properties of Gaussian ensembles are studied in detail in the regimes of weak and strong non-Hermiticity.
متن کاملMassive partition functions and complex eigenvalue correlations in Matrix Models with symplectic symmetry
We compute all massive partition functions or characteristic polynomials and their complex eigenvalue correlation functions for non-Hermitean extensions of the symplectic and chiral symplectic ensemble of random matrices. Our results are valid for general weight functions without degeneracies of the mass parameters. The expressions we derive are given in terms of the Pfaffian of skew orthogonal...
متن کاملNon-Hermitean Wishart random matrices (I)
A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real-quaternion) stochastic time series representing two ‘remote’ complex systems. The first paper in a series provides a detailed spectral theory of non-Hermitean Wishart random matrices composed of complex valued entries. The great em...
متن کاملNon-Hermitean Random Matrix Theory: Summation of Planar Diagrams, the “Single-Ring” Theorem and the Disk-Annulus Phase Transition
I review aspects of work done in collaboration with A. Zee and R. Scalettar [1, 2, 3] on complex non-hermitean random matrices. I open by explaining why the bag of tools used regularly in analyzing hermitean random matrices cannot be applied directly to analyze non-hermitean matrices, and then introduce the Method of Hermitization, which solves this problem. Then, for rotationally invariant ens...
متن کاملNON-HERMITEAN RANDOM MATRIX THEORY: method of hermitean reduction
We consider random non-hermitean matrices in the large N limit. The power of analytic function theory cannot be brought to bear directly to analyze non-hermitean random matrices, in contrast to hermitean random matrices. To overcome this difficulty, we show that associated to each ensemble of nonhermitean matrices there is an auxiliary ensemble of random hermitean matrices which can be analyzed...
متن کامل