相关论文: Eigenvalue distributions for some correlated compl…

Pencils of Hankel matrices whose elements have a joint Gaussian distribution with nonzero mean and not identical covariance are considered. An approximation to the distribution of the squared modulus of their determinant is computed which…

A recent conjecture regarding the average of the minimum eigenvalue of the reduced density matrix of a random complex state is proved. In fact, the full distribution of the minimum eigenvalue is derived exactly for both the cases of a…

We derive efficient recursive formulas giving the exact distribution of the largest eigenvalue for finite dimensional real Wishart matrices and for the Gaussian Orthogonal Ensemble (GOE). In comparing the exact distribution with the…

The sum of Wishart matrices has an important role in multiuser communication employing multiantenna elements, such as multiple-input multiple-output (MIMO) multiple access channel (MAC), MIMO Relay channel, and other multiuser channels…

We compute analytically, for large N, the probability distribution of the number of positive eigenvalues (the index N_{+}) of a random NxN matrix belonging to Gaussian orthogonal (\beta=1), unitary (\beta=2) or symplectic (\beta=4)…

We derive Painlev\'e--type expressions for the distribution of the $m^{th}$ largest eigenvalue in the Gaussian Orthogonal and Symplectic Ensembles in the edge scaling limit. The work of Johnstone and Soshnikov (see [7], [10]) implies the…

We study the evolution of the distribution of eigenvalues of $N\times N$ matrix ensembles subject to a change of variances of its matrix elements. Our results indicate that the evolution of the probability density is governed by a Fokker-…

The determinant of the Gaussian unitary ensemble matrix is show to be distributed as a product of independent chi random variables with parameters $1,3,3,5,5,\dots.$

The eigenvalue statistics for complex $N \times N$ Wishart matrices $X_{r,s}^\dagger X_{r,s}$, where $ X_{r,s}$ is equal to the product of $r$ complex Gaussian matrices, and the inverse of $s$ complex Gaussian matrices, are considered. In…

In this paper, we use a new approach to prove that the largest eigenvalue of the sample covariance matrix of a normally distributed vector is bigger than the true largest eigenvalue with probability 1 when the dimension is infinite. We…

In this note, we define a Gaussian probability distribution over matrices. We prove some useful properties of this distribution, namely, the fact that marginalization, conditioning, and affine transformations preserve the matrix Gaussian…

We describe a method to determine the eigenvalue density of empirical covariance matrix in the presence of correlations between samples. This is a straightforward generalization of the method developed earlier by the authors for…

We give formulae for first and second derivatives of generalized eigenvalues/eigenvectors of symmetric matrices and generalized singular values/singular vectors of rectangular matrices when the matrices are linear or nonlinear functions of…

Eigenvectors of matrices on a network have been used for understanding spectral clustering and influence of a vertex. For matrices with small geodesic-width, we propose a distributed iterative algorithm in this letter to find eigenvectors…

The remarkable universality of the eigenvalue correlation functions is perhaps one of the most salient findings in random matrix theory. Particularly for short-range separations of the eigenvalues, the correlation functions have been shown…

Consider the product of $m$ independent $n\times n$ random matrices from the spherical ensemble for $m\ge 1$. The empirical distribution based on the $n$ eigenvalues of the product is called the empirical spectral distribution. Two recent…

Eigenvectors associated with non-degenerate eigenvalues are shown to correspond to columns of the adjugate of the characteristic matrix. Degenerate eigenvalues are associated with eigenvectors that correspond to reduced complement tensors…

We rederive in a simplified version the Lehmann-Sommers eigenvalue distribution for the Gaussian ensemble of asymmetric real matrices, invariant under real orthogonal transformations, as a basis for a detailed derivation of a Pfaffian…

Assume a finite set of complex random variables form a determinantal point process, we obtain a theorem on the limit of the empirical distribution of these random variables. The result is applied to %We study the limits of the empirical…

We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…