Multiplicative convolution of real asymmetric and real anti-symmetric matrices

Kieburg M, Forrester PJ, Ipsen JR (2019)
ADVANCES IN PURE AND APPLIED MATHEMATICS 10(4): 467-492.

Zeitschriftenaufsatz | Veröffentlicht| Englisch

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Autor/in
Kieburg, MarioUniBi; Forrester, Peter J.; Ipsen, Jesper R.
Einrichtung
Abstract / Bemerkung
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 ... X(2)X(1)AX(1)(T)X(2)(T) ... X-M(T), where each X-i is a standard real Gaussian matrix and A is real anti-symmetric, exhibits analogous properties. Here we use the theory of spherical functions and transforms to present a theory which, for even dimensions, includes these properties of the latter product as a special case. As an example we show that the theory also allows for a treatment of this class of Hermitised product when the X-i are chosen as sub-blocks of Haar distributed real orthogonal matrices.
Stichworte
Products of random matrices; spherical function; bi-orthogonal; functions; matrix integrals
Erscheinungsjahr
2019
Zeitschriftentitel
ADVANCES IN PURE AND APPLIED MATHEMATICS
Band
10
Ausgabe
4
Seite(n)
467-492
ISSN
1867-1152
eISSN
1869-6090
Page URI
https://pub.uni-bielefeld.de/record/2938380

Zitieren

Kieburg M, Forrester PJ, Ipsen JR. Multiplicative convolution of real asymmetric and real anti-symmetric matrices. ADVANCES IN PURE AND APPLIED MATHEMATICS. 2019;10(4):467-492.
Kieburg, M., Forrester, P. J., & Ipsen, J. R. (2019). Multiplicative convolution of real asymmetric and real anti-symmetric matrices. ADVANCES IN PURE AND APPLIED MATHEMATICS, 10(4), 467-492. doi:10.1515/apam-2018-0037
Kieburg, M., Forrester, P. J., and Ipsen, J. R. (2019). Multiplicative convolution of real asymmetric and real anti-symmetric matrices. ADVANCES IN PURE AND APPLIED MATHEMATICS 10, 467-492.
Kieburg, M., Forrester, P.J., & Ipsen, J.R., 2019. Multiplicative convolution of real asymmetric and real anti-symmetric matrices. ADVANCES IN PURE AND APPLIED MATHEMATICS, 10(4), p 467-492.
M. Kieburg, P.J. Forrester, and J.R. Ipsen, “Multiplicative convolution of real asymmetric and real anti-symmetric matrices”, ADVANCES IN PURE AND APPLIED MATHEMATICS, vol. 10, 2019, pp. 467-492.
Kieburg, M., Forrester, P.J., Ipsen, J.R.: Multiplicative convolution of real asymmetric and real anti-symmetric matrices. ADVANCES IN PURE AND APPLIED MATHEMATICS. 10, 467-492 (2019).
Kieburg, Mario, Forrester, Peter J., and Ipsen, Jesper R. “Multiplicative convolution of real asymmetric and real anti-symmetric matrices”. ADVANCES IN PURE AND APPLIED MATHEMATICS 10.4 (2019): 467-492.

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