Non-Hermitean Wishart random matrices (I)

Details Non-Hermitean Wishart random matrices (I) Non-Hermitean Wishart random matrices (I)

2010-06-15

arxiv.org/abs/1006.3096v2

J. Math. Phys. 51: 103510,2010

Physics

Mathematical Physics

published version: 29 pages, 4 figures; references added

Scientific paper

10.1063/1.3483455

A non-Hermitean extension of paradigmatic Wishart random matrices is introduced to set up a theoretical framework for statistical analysis of (real, complex and real quaternion) stochastic time series representing two "remote" complex systems. The first paper in a series provides a detailed spectral theory of non-Hermitean Wishart random matrices composed of complex valued entries. The great emphasis is placed on an asymptotic analysis of the mean eigenvalue density for which we derive, among other results, a complex-plane analogue of the Marchenko-Pastur law. A surprising connection with a class of matrix models previously invented in the context of quantum chromodynamics is pointed out.

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