title: Spectral density of a Wishart model for nonsymmetric correlation matrices.
abstract: The Wishart model for real symmetric correlation matrices is defined as W=AA^{t}, where matrix A is usually a rectangular Gaussian random matrix and A^{t} is the transpose of A. Analogously, for nonsymmetric correlation matrices, a model may be defined for two statistically equivalent but different matrices A and B as AB^{t}. The corresponding Wishart model, thus, is defined as C=AB^{t}BA^{t}. We study the spectral density of C for the case when A and B are not statistically independent. The ensemble average of such nonsymmetric matrices, therefore, does not simply vanishes to a null matrix. In this paper we derive a Pastur self-consistent equation which describes spectral density of C at large matrix dimension. We complement our analytic results with numerics.
authors.affiliation: Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, C.P. 62210 Cuernavaca, México.
authors.lastname: Vinayak