1306.2242 (Vinayak)

Spectral density of a Wishart model for nonsymmetric Correlation
Matrices    [PDF]

Vinayak

Wishart model for real symmetric correlation matrices is defined as $\mathsf{W}=\mathsf{AA}^{t}$, where matrix $\mathsf{A}$ is usually a rectangular Gaussian random matrix and $\mathsf{A}^{t}$ is the transpose of $\mathsf{A}$. Analogously, for nonsymmetric correlation matrices, a model may be defined for two statistically identical but different matrices $\mathsf{A}$ and $\mathsf{B}$ as $\mathsf{AB}^{t}$. The corresponding Wishart model, thus, is defined as $\mathbf{C}=\mathsf{AB}^{t}\mathsf{BA}^{t}$. Spectral density of $\mathbf{C}$ has been calculated for the case when $\mathsf{A}$ and $\mathsf{B}$ are not statistically independent. The ensemble average of such nonsymmetric matrices, therefore, does not simply vanishes to a null matrix. Analytic expression for the spectral density is obtained for large $\mathbf{C}$. Some numerical examples have been presented to verify the result.

View original: http://arxiv.org/abs/1306.2242