Related papers: De Finetti-Style Results for Wishart Matrices: Com…
We prove that the number of iterations required to solve a random positive definite linear system with the conjugate gradient algorithm is almost deterministic for large matrices. We treat the case of Wishart matrices $W = XX^*$ where $X$…
Let $X_1,..., X_n \in \mathbb{R}^d$ be independent Gaussian random vectors with independent entries and variance profile $(b_{ij})_{i \in [d],j \in [n]}$. A major question in the study of covariance estimation is to give precise control on…
In this paper we consider non-asymptotic behavior of the real compound Wishart matrices that generalize the classical real Wishart distribution. In particular, we consider matrices of the form 1/nXBX', where X consists of real centered…
We consider symmetric and Hermitian random matrices whose entries are independent and symmetric random variables with an arbitrary variance pattern. Under a novel Short-to-Long Mixing condition, which is sharp in the sense that it precludes…
We study information-theoretic phase transitions for the detectability of latent geometry in bipartite random geometric graphs RGGs with Gaussian d-dimensional latent vectors while only a subset of edges carries latent information…
The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large…
Random graphs with latent geometric structure are popular models of social and biological networks, with applications ranging from network user profiling to circuit design. These graphs are also of purely theoretical interest within…
We study a system of $N$ non-intersecting $(1+1)$-dimensional fluctuating elastic interfaces (`vicious bridges') at thermal equilibrium, each subject to periodic boundary condition in the longitudinal direction and in presence of a…
We consider four nontrivial ensembles involving Gaussian Wigner and Wishart matrices. These are relevant to problems ranging from multiantenna communication to random supergravity. We derive the matrix probability density, as well as the…
Gaussian graphical models are a popular tool to learn the dependence structure in the form of a graph among variables of interest. Bayesian methods have gained in popularity in the last two decades due to their ability to simultaneously…
Using Beck and Cohen's superstatistics, we introduce in a systematic way a family of generalised Wishart-Laguerre ensembles of random matrices with Dyson index $\beta$ = 1,2, and 4. The entries of the data matrix are Gaussian random…
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.…
Wishart random matrices with a sparse or diluted structure are ubiquitous in the processing of large datasets, with applications in physics, biology and economy. In this work we develop a theory for the eigenvalue fluctuations of diluted…
We study the asymptotic behavior of eigenvalues of large complex correlated Wishart matrices at the edges of the limiting spectrum. In this setting, the support of the limiting eigenvalue distribution may have several connected components.…
We compute analytically the probability of large fluctuations to the left of the mean of the largest eigenvalue in the Wishart (Laguerre) ensemble of positive definite random matrices. We show that the probability that all the eigenvalues…
The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this…
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…
Matrix Schubert varieties are certain varieties in the affine space of square matrices which are determined by specifying rank conditions on submatrices. We study these varieties for generic matrices, symmetric matrices, and upper…
Marginal likelihood, also known as model evidence, is a fundamental quantity in Bayesian statistics. It is used for model selection using Bayes factors or for empirical Bayes tuning of prior hyper-parameters. Yet, the calculation of…
The correlated Wishart model provides the standard benchmark when analyzing time series of any kind. Unfortunately, the real case, which is the most relevant one in applications, poses serious challenges for analytical calculations. Often…