Eigenvalue distributions for some correlated complex sample covariance matrices

Abstract

The distributions of the smallest and largest eigenvalues for the matrix product $Z^{†}Z$, where $Z$ is an $n\times m$ complex Gaussian matrix with correlations both along rows and down columns, are expressed as $m\times m$ determinants. In the case of correlation along rows, these expressions are computationally more efficient than those involving sums over partitions and Schur polynomials reported recently for the same distributions.

11 pages

References in corpus (3)

• A rate of convergence result for the largest eigenvalue of complex white Wishart matrices
• Eigenvalue Density of Correlated Complex Random Wishart Matrices
• The Efficient Evaluation of the Hypergeometric Function of a Matrix Argument

Cited by in corpus (9)

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• Distribution of the Smallest Eigenvalue in the Correlated Wishart Model
• Recursion scheme for the largest $\beta$-Wishart-Laguerre eigenvalue and Landauer conductance in quantum transport
• Recursion for the smallest eigenvalue density of $\beta$-Wishart-Laguerre ensemble
• Smallest eigenvalue density for regular or fixed-trace complex Wishart-Laguerre ensemble and entanglement in coupled kicked tops
• Distribution of the Smallest Eigenvalue in Complex and Real Correlated Wishart Ensembles
• The Correlated Jacobi and the Correlated Cauchy-Lorentz ensembles