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Please use this identifier to cite or link to this item: http://bura.brunel.ac.uk/handle/2438/3954

Title: The chiral Gaussian two-matrix ensemble of real asymmetric matrices
Authors: Akemann, G
Phillips, MJ
Sommers, HJ
Keywords: Chiral
Real asymmetric matrices
Two-matrix ensemble
Publication Date: 2009
Abstract: We solve a family of Gaussian two-matrix models with rectangular Nx(N+nu) matrices,having real asymmetric matrix elements and depending on a non-Hermiticity parameter mu. Our model can be thought of asxthe chiral extension of the real Ginibre ensemble, relevant for Dirac operators in the same symmetry class. It has the property that its eigenvalues are either real, purely imaginary, or come in complex conjugate eigenvalue pairs. The eigenvalue joint probability distribution for our model is explicitly computed, leading to a non-Gaussian distribution including K-Bessel functions. All n-point density correlation functions are expressed for finite N in terms of a Pfaffian form. This contains a kernel involving Laguerre polynomials in the complex plane as a building block which was previously computed by the authors. This kernel can be expressed in terms of the kernel for complex non-Hermitian matrices, generalising the known relation among ensembles of Hermitian random matrices. Compact expressions are given for the density at finite N as an example, as well as its microscopic large-N limits at the origin for fixed nu at strong and weak non-Hermiticity.
URI: http://uk.arxiv.org/abs/0911.1276
http://bura.brunel.ac.uk/handle/2438/3954
Appears in Collections:Mathematical Physics
Dept of Mathematics Research Papers

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