Non-Hermitean Wishart random matrices (I)

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.

published version: 29 pages, 4 figures; references added

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Cited by in corpus (12)

• Weak Commutation Relations and Eigenvalue Statistics for Products of Rectangular Random Matrices
• Singular value statistics of matrix products with truncated unitary matrices
• Universal microscopic correlation functions for products of independent Ginibre matrices
• Universal microscopic correlation functions for products of truncated unitary matrices
• Products of Independent Quaternion Ginibre Matrices and their Correlation Functions
• A non-Hermitian generalisation of the Marchenko-Pastur distribution: from the circular law to multi-criticality
• Probability of all eigenvalues real for products of standard Gaussian matrices
• Asymmetric correlation matrices: an analysis of financial data
• Spectral Domain of Large Nonsymmetric Correlated Wishart Matrices
• Summing free unitary random matrices
• Integrable Aspects of Universal Quantum Transport in Chaotic Cavities
• A path integral approach to sparse non-Hermitian random matrices