Related papers: Chi-square approximation for the distribution of i…
In this study, we derive the exact distributions of eigenvalues of a singular Wishart matrix under an elliptical model. We define generalized heterogeneous hypergeometric functions with two matrix arguments and provide convergence…
The sum of independent Wishart matrices, taken from distributions with unequal covariance matrices, plays a crucial role in multivariate statistics, and has applications in the fields of quantitative finance and telecommunication. However,…
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…
In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of…
This paper deals with the asymptotic distribution of Wishart matrix and its application to the estimation of the population matrix parameter when the population eigenvalues are block-wise infinitely dispersed. We show that the appropriately…
Wishart random matrix theory is of major importance for the analysis of correlated time series. The distribution of the smallest eigenvalue for Wishart correlation matrices is particularly interesting in many applications. In the complex…
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 eigenvalue densities of two random matrix ensembles, the Wigner Gaussian matrices and the Wishart covariant matrices, are decomposed in the contributions of each individual eigenvalue distribution. It is shown that the fluctuations of…
This paper proposes a unified approach that enables the Wishart distribution to be studied simultaneously in the real, complex, quaternion and octonion cases. In particular, the noncentral generalised Wishart distribution, the joint density…
We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant…
We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for the general dimension. The formula is expressed in terms of a definite integral with…
In this paper we study the distribution of the scaled largest eigenvalue of complexWishart matrices, which has diverse applications both in statistics and wireless communications. Exact expressions, valid for any matrix dimensions, have…
In this article, we obtain an equation for the high-dimensional limit measure of eigenvalues of generalized Wishart processes, and the results is extended to random particle systems that generalize SDEs of eigenvalues. We also introduce a…
Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B…
Wishart correlation matrices are the standard model for the statistical analysis of time series. The ensemble averaged eigenvalue density is of considerable practical and theoretical interest. For complex time series and correlation…
In \cite{Diaz} beta type I and II doubly singular distributions were introduced and their densities and the joint densities of nonzero eigenvalues were derived. In such matrix variate distributions $p$, the dimension of two singular Wishart…
The eigenvalue distribution is investigated for matrix models related via the localization to Chern-Simons-matter theories. An integral representation of the planar resolvent is used to derive the positions of the branch points of the…
The paper "An efficient sampling scheme for the eigenvalues of dual Wishart matrices", by I.~Santamar\'ia and V.~Elvira, [\emph{IEEE Signal Processing Letters}, vol.~28, pp.~2177--2181, 2021] \cite{SE21}, poses the question of efficient…
Random matrix theory has become a cornerstone in modern statistics and data science, providing fundamental tools for understanding high-dimensional covariance structures. Within this framework, the Wishart matrix plays a central role in…
In this work, we consider the weighted difference of two independent complex Wishart matrices and derive the joint probability density function of the corresponding eigenvalues in a finite-dimension scenario using two distinct approaches.…