Journal article

Multiplicative convolution of real asymmetric and real anti-symmetric matrices

Mario Kieburg, Peter J Forrester, Jesper R Ipsen

Advances in Pure and Applied Mathematics | WALTER DE GRUYTER GMBH | Published : 2019

Abstract

Abstract The singular values of products of standard complex Gaussian random matrices, or sub-blocks of Haar distributed unitary matrices, have the property that their probability distribution has an explicit, structured form referred to as a polynomial ensemble. It is furthermore the case that the corresponding bi-orthogonal system can be determined in terms of Meijer G-functions, and the correlation kernel given as an explicit double contour integral. It has recently been shown that the Hermitised product {X_{M}\cdots X_{2}X_{1}AX_{1}^{T}X_{2}^{T}\cdots X_{M}^{T}} ..

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Grants

Awarded by Australian Research Council


Awarded by German research council (DFG)


Funding Acknowledgements

We acknowledge support by the Australian Research Council through grant DP170102028 (PJF), the ARC Centre of Excellence for Mathematical and Statistical Frontiers (PJF,JRI,MK), and the German research council (DFG) via the CRC 1283: "Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications".