Non-Hermitean Wishart random matrices (I)

Eugene Kanzieper and Navinder Singh

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Abstract: 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.

Date: 2010-06, Revised 2010-10
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Published in J. Math. Phys. 51: 103510,2010

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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:1006.3096

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