2013
DOI: 10.1103/physreve.88.052118
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Products of rectangular random matrices: Singular values and progressive scattering

Abstract: 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 for all correlation functions and moments for finite matrix sizes are obtained using a two-matrix model and the method of biorthogonal polynomials. This ge… Show more

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Cited by 176 publications
(384 citation statements)
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“…This was extended by Akemann, Ipsen and Kieburg [4] to the general rectangular case. The determinantal point process is a biorthogonal ensemble [13] with joint probability density function (see [4, formula (18)])…”
Section: Products Of Ginibre Random Matricesmentioning
confidence: 98%
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“…This was extended by Akemann, Ipsen and Kieburg [4] to the general rectangular case. The determinantal point process is a biorthogonal ensemble [13] with joint probability density function (see [4, formula (18)])…”
Section: Products Of Ginibre Random Matricesmentioning
confidence: 98%
“…Very recently, Akemann, Kieburg, and Wei [5] found that the squared singular values of products of complex Ginibre matrices are a determinantal point process on the positive real line. This was further extended to the case of products of rectangular Ginibre matrices by Akemann, Ipsen and Kieburg [4]. The correlation kernels in [2,3,4,5,25] are all expressed in terms of Meijer G-functions.…”
Section: Products Of Ginibre Random Matricesmentioning
confidence: 99%
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