Non-Hermitian Random Matrix Ensembles

Abstract

This is a concise review of the complex, real and quaternion real Ginibre random matrix ensembles and their elliptic deformations. Eigenvalue correlations are exactly reduced to two-point kernels and discussed in the strongly and weakly non-Hermitian limits of large matrix size.

23 pages, invited article for the Oxford Handbook of Random Matrix Theory

References in corpus (1)

• Random matrices: Universality of ESDs and the circular law

Cited by in corpus (13)

• Random-matrix theory of Majorana fermions and topological superconductors
• Induced Ginibre ensemble of random matrices and quantum operations
• Dysonian dynamics of the Ginibre ensemble
• Universal microscopic correlation functions for products of truncated unitary matrices
• Extremes of $2d$ Coulomb gas: universal intermediate deviation regime
• The Interpolating Airy Kernels for the beta=1 and beta=4 Elliptic Ginibre Ensembles
• Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels
• Interpolation between Airy and Poisson statistics for unitary chiral non-Hermitian random matrix ensembles
• Non-Hermitian extensions of Wishart random matrix ensembles
• Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble
• Families of two-dimensional Coulomb gases on an ellipse: correlation functions and universality
• Composition of quantum operations and products of random matrices
• Mixed Moments for the Product of Ginibre Matrices