相关论文: The asymptotic distribution of the determinant of …

This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…

Sample correlation matrices are employed ubiquitously in statistics. However, quite surprisingly, little is known about their asymptotic spectral properties for high-dimensional data, particularly beyond the case of "null models" for which…

We place ourselves in the setting of high-dimensional statistical inference, where the number of variables $p$ in a data set of interest is of the same order of magnitude as the number of observations $n$. More formally, we study the…

Complex systems are typically represented by large ensembles of observations. Correlation matrices provide an efficient formal framework to extract information from such multivariate ensembles and identify in a quantifiable way patterns of…

Random matrices now play a role in many parts of computational mathematics. To advance these applications, it is desirable to have tools that are flexible, easy to use, and powerful. Over the last 25 years, researchers have developed a…

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…

The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…

The paper deals with distribution of singular values of product of random matrices arising in the analysis of deep neural networks. The matrices resemble the product analogs of the sample covariance matrices, however, an important…

We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…

We derive analytic expressions for infinite products of random 2x2 matrices. The determinant of the target matrix is log-normally distributed, whereas the remainder is a surprisingly complicated function of a parameter characterizing the…

In this article, we define the matricization of a tensor and we present some properties of the matricization. After that, we define the determinant of a tensor and we present some properties of the determinant. We define the covariance…

We study the distribution of singular values of product of random matrices pertinent to the analysis of deep neural networks. The matrices resemble the product of the sample covariance matrices, however, an important difference is that the…

We study limit distributions of independent random matrices as well as limit joint distributions of their blocks under normalized partial traces composed with classical expectation. In particular, we are concerned with the ensemble of…

This review article provides an overview of random matrix theory (RMT) with a focus on its growing impact on the formulation and inference of statistical models and methodologies. Emphasizing applications within high-dimensional statistics,…

Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…

We consider large random matrices with a general slowly decaying correlation among its entries. We prove universality of the local eigenvalue statistics and optimal local laws for the resolvent away from the spectral edges, generalizing the…

Synchronized measurements of a large power grid enable an unprecedented opportunity to study the spatialtemporal correlations. Statistical analytics for those massive datasets start with high-dimensional data matrices. Uncertainty is…

We study the convergence properties of a pair of learning algorithms (learning with and without memory). This leads us to study the dominant eigenvalue of a class of random matrices. This turns out to be related to the roots of the…

We determine the probability that a random n x n symmetric matrix over {1, 2, ... , m} has determinant divisible by m.

We analyze the spectral distribution of symmetric random matrices with correlated entries. While we assume that the diagonals of these random matrices are stochastically independent, the elements of the diagonals are taken to be correlated.…