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Non-Hermitean Wishart random matrices (I)

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  • Eugene Kanzieper
  • Navinder Singh

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.

Suggested Citation

  • Eugene Kanzieper & Navinder Singh, 2010. "Non-Hermitean Wishart random matrices (I)," Papers 1006.3096, arXiv.org, revised Oct 2010.
    • Handle: RePEc:arx:papers:1006.3096
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