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We discuss the product of M rectangular random matrices with independent Gaussian entries, which have several applications, including wireless telecommunication and econophysics. For complex matrices an explicit expression for the joint probability density function is obtained using the Harish-Chandra-Itzykson-Zuber integration formula. Explicit expressions(More)
We consider the product of M quadratic random matrices with complex elements and no further symmetry, where all matrix elements of each factor have a Gaussian distribution. This generalises the classical Wishart-Laguerre Gaussian Unitary Ensemble with M = 1. In this paper we first compute the joint probability distribution for the singular values of the(More)
We study the joint probability density of the eigenvalues of a product of rectangular real, complex, or quaternion random matrices in a unified way. The random matrices are distributed according to arbitrary probability densities, whose only restriction is the invariance under left and right multiplication by orthogonal, unitary, or unitary symplectic(More)
Wishart correlation matrices are the standard model for the statistical analysis of time series. The ensemble averaged eigenvalue density is of considerable practical and theoretical interest. For complex time series and correlation matrices, the eigenvalue density is known exactly. In the real case, a fundamental mathematical obstacle made it forbiddingly(More)
We find the lattice spacing dependence of the eigenvalue density of the non-Hermitian Wilson Dirac operator in the ϵ domain. The starting point is the joint probability density of the corresponding random matrix theory. In addition to the density of the complex eigenvalues we also obtain the density of the real eigenvalues separately for positive and(More)
Recently, two different approaches were put forward to extend the supersymmetry method in random matrix theory from Gaussian ensembles to general rotation invariant ensembles. These approaches are the generalized Hubbard– Stratonovich transformation and the superbosonization formula. Here, we prove the equivalence of both approaches. To this end, we reduce(More)
Recently, the supersymmetry method was extended from Gaussian ensembles to arbitrary unitarily invariant matrix ensembles by generalizing the Hubbard–Stratonovich transformation. Here, we complete this extension by including arbitrary orthogonally and unitary–symplectically invariant matrix ensembles. The results are equivalent to, but the approach is(More)
Rectangular real N×(N+ν) matrices W with a Gaussian distribution appear very frequently in data analysis, condensed matter physics, and quantum field theory. A central question concerns the correlations encoded in the spectral statistics of WW^{T}. The extreme eigenvalues of WW^{T} are of particular interest. We explicitly compute the distribution and the(More)
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