We give an overview of random matrix theory (RMT) with the objective of highlighting the
results and concepts that have a growing impact in the formulation and inference 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 …

The aim of this book is to investigate the spectral properties of random matrices (RM) when
their dimensions tend to infinity. All classical limiting theorems in statistics are under the …

The idea for this book came from the time the authors spent at the Statistics and Applied
Mathematical Sciences Institute (SAMSI) in Research Triangle Park in North Carolina …

With the rapid development of modern computing techniques, statisticians are dealing with
data with much higher dimension. Consequently, due to their loss of accuracy or power …

We develop a new estimator of the number of factors in the approximate factor models. The
estimator works well even when the idiosyncratic terms are substantially correlated. It is …

This book presents a unified theory of random matrices for applications in machine learning,
offering a large-dimensional data vision that exploits concentration and universality …

The classical random matrix theory is mostly focused on asymptotic spectral properties of
random matrices as their dimensions grow to infinity. At the same time many recent …

Abstract Let where Xn=(Xij) is n× N with iid complex standardized entries having finite fourth
moment, and is a Hermitian square root of the nonnegative definite Hermitian matrix Tn. The …

In this paper, the authors show that the smallest (if p≤ n) or the (p-n+ 1)-th smallest (if p> n)
eigenvalue of a sample covariance matrix of the form (1/n) XX'tends almost surely to the limit …