Correlation Functions of Asymmetric Real Matrices

Abstract

We give a closed form for the correlation functions of ensembles of asymmetric real matrices in terms of the Pfaffian of an antisymmetric matrix formed from a $2\times 2$ matrix kernel associated to the ensemble. We also derive closed forms for the matrix kernel and correlation functions for Ginibre's real ensemble.

34 pages. This revision contains new content and some corrections

References in corpus (5)

• Eigenvalue statistics of the real Ginibre ensemble
• Correlation functions for symmetrized increasing subsequences
• Statistics of Real Eigenvalues in Ginibre's Ensemble of Random Real Matrices
• Representation theory and random point processes
• Random Matrices: The circular Law

Cited by in corpus (6)

• Random matrices: Universality of local spectral statistics of non-Hermitian matrices
• A new approach to derive Pfaffian structures for random matrix ensembles
• Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles
• Correlation Functions for β=1 Ensembles of Matrices of Odd Size
• Asymptotic Coincidence of the Statistics for Degenerate and Non-Degenerate Correlated Real Wishart Ensembles
• O(N) colour-flavour transformations and characteristic polynomials of real random matrices