Skew orthogonal polynomials and the partly symmetric real Ginibre ensemble

DOI10.1088/1751-8113/41/37/375003zbMath1185.15032arXiv0806.0055OpenAlexW2082523211MaRDI QIDQ3528198

Taro Nagao, Peter J. Forrester

Publication date: 8 October 2008

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.0055

zbMATH Keywords

orthogonal polynomialseigenvaluesHermite polynomialsGaussian random matricescorrelationsGinibre ensemblePfaffian formula

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Eigenvalues, singular values, and eigenvectors (15A18) Random matrices (algebraic aspects) (15B52)

Related Items (21)

Correlation functions for \(\beta =1\) ensembles of matrices of odd size ⋮ The real Ginibre ensemble with \(k=O(n)\) real eigenvalues ⋮ Pfaffian point process for the Gaussian real generalised eigenvalue problem ⋮ Spherical induced ensembles with symplectic symmetry ⋮ Fluctuations and correlations for products of real asymmetric random matrices ⋮ Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble ⋮ Almost-Hermitian random matrices and bandlimited point processes ⋮ Nonlinear analogue of the May−Wigner instability transition ⋮ Central limit theorems for the real eigenvalues of large Gaussian random matrices ⋮ Condition numbers for real eigenvalues in the real elliptic Gaussian ensemble ⋮ Topology trivialization transition in random non-gradient autonomous ODEs on a sphere ⋮ Real eigenvalue statistics for products of asymmetric real Gaussian matrices ⋮ On statistics of bi-orthogonal eigenvectors in real and complex Ginibre ensembles: combining partial Schur decomposition with supersymmetry ⋮ Spectral radii of large non-Hermitian random matrices ⋮ GUE-chGUE transition preserving chirality at finite matrix size ⋮ The interpolating Airy kernels for the \(\beta=1\) and \(\beta=4\) elliptic Ginibre ensembles ⋮ Extremal laws for the real Ginibre ensemble ⋮ The probability that all eigenvalues are real for products of truncated real orthogonal random matrices ⋮ A method to calculate correlation functions for \(\beta =1\) random matrices of odd size ⋮ The Ginibre ensemble of real random matrices and its scaling limits ⋮ How Many Eigenvalues of a Product of Truncated Orthogonal Matrices are Real?

This page was built for publication: Skew orthogonal polynomials and the partly symmetric real Ginibre ensemble