Related papers: Spiked Models in Wishart Ensemble
We study ensembles of random symmetric matrices whose entries exhibit certain correlations. Examples are distributions of Curie-Weiss-type. We provide a criterion on the correlations ensuring the validity of Wigner's semicircle law for the…
Consider two $p$-variate populations, not necessarily Gaussian, with covariance matrices $\Sigma_1$ and $\Sigma_2$, respectively, and let $S_1$ and $S_2$ be the sample covariances matrices from samples of the populations with degrees of…
High-dimensional autocovariance matrices play an important role in dimension reduction for high-dimensional time series. In this article, we establish the central limit theorem (CLT) for spiked eigenvalues of high-dimensional sample…
We are interested in the distribution of Wishart samples after forgetting their scaling factors. We call such a distribution a projective Wishart distribution. We show that projective Wishart distributions have strong links with the…
This paper studies the related problems of prediction, covariance estimation, and principal component analysis for the spiked covariance model with heteroscedastic noise. We consider an estimator of the principal components based on…
We consider a Wigner-type ensemble, i.e. large hermitian $N\times N$ random matrices $H=H^*$ with centered independent entries and with a general matrix of variances $S_{xy}=\mathbb E|H_{xy}|^2$. The norm of $H$ is asymptotically given by…
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…
The Wishart distribution and its generalizations are among the most prominent probability distributions in multivariate statistical analysis, arising naturally in applied research and as a basis for theoretical models. In this paper, we…
We study a well-known problem concerning a random variable $Z$ uniformly distributed between two independent random variables. A new extension has been introduced for this problem and fairly large classes of randomly weighted average…
Triplet extensions are attractive alternatives to the standard model (SM) of particle physics. While models with only one triplet are highly constrained by electroweak precision observables, this is not necessarily the case once several…
We study the statistical properties of the complex generalization of Wigner time delay $\tau_\text{W}$ for sub-unitary wave chaotic scattering systems. We first demonstrate theoretically that the mean value of the $\text{Re}[\tau_\text{W}]$…
We study symmetric spiked matrix models with respect to a general class of noise distributions. Given a rank-1 deformation of a random noise matrix, whose entries are independently distributed with zero mean and unit variance, the goal is…
We consider the $2$-spin spherical Sherrington--Kirkpatrick model whose disorder is given by a deformed Wigner matrix of the form $W+\lambda V$, where $W$ is a Wigner matrix and $V$ is a random diagonal matrix with i.i.d. entries. Assuming…
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…
We consider the singular value statistics of products of independent random matrices. In particular we compute the corresponding averages of products of characteristic polynomials. To this aim we apply the projection formula recently…
We consider the conjugate gradient algorithm applied to a general class of spiked sample covariance matrices. The main result of the paper is that the norms of the error and residual vectors at any finite step concentrate on deterministic…
The statistical properties of coherent radiation scattered from phase-ordering materials are studied in detail using large-scale computer simulations and analytic arguments. Specifically, we consider a two-dimensional model with a…
Covariance matrices provide a valuable source of information about complex interactions and dependencies within the data. However, from a clustering perspective, this information has often been underutilized and overlooked. Indeed, commonly…
In wavefront shaping, waves are focused through complex media onto one or more target points, and the resulting intensity enhancement is quantified by the enhancement factor. While reproducible enhancement is crucial in experiments, the…
We describe a general expansion of spherical (full-sky) bispectra into a set of orthogonal modes. For squeezed shapes, the basis separates physically-distinct signals and is dominated by the lowest moments. In terms of reduced bispectra, we…