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The Oxford Handbook of Random Matrix Theory
I INTRODUCTION II PROPERTIES OF RANDOM MATRIX THEORY III APPLICATIONS OF RANDOM MATRIX THEORY
Products of rectangular random matrices: singular values and progressive scattering.
- G. Akemann, J. R. Ipsen, M. Kieburg
- MathematicsPhysical review. E, Statistical, nonlinear, and…
- 29 July 2013
The so-called ergodic mutual information is considered, which gives an upper bound for the spectral efficiency of a MIMO communication channel with multifold scattering.
Higher genus correlators for the Hermitian matrix model with multiple cuts
- G. Akemann
- 3 June 1996
Singular value correlation functions for products of Wishart random matrices
This paper first compute the joint probability distribution for the singular values of the product matrix when the matrix size N and the number M are fixed but arbitrary, which leads to a determinantal point process which can be realized in two different ways.
Universal microscopic correlation functions for products of independent Ginibre matrices
We consider the product of n complex non-Hermitian, independent random matrices, each of size N × N with independent identically distributed Gaussian entries (Ginibre matrices). The joint probability…
Wilson loops in N = 4 supersymmetric Yang–Mills theory from random matrix theory
Integrable Structure of Ginibre’s Ensemble of Real Random Matrices and a Pfaffian Integration Theorem
Abstract In the recent publication (E. Kanzieper and G. Akemann in Phys. Rev. Lett. 95:230201, 2005), an exact solution was reported for the probability pn,k to find exactly k real eigenvalues in the…
Multicritical Microscopic Spectral Correlators of Hermitian and Complex Matrices
A new chiral two-matrix theory for Dirac spectra with imaginary chemical potential