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 …

These notes are based on lectures delivered by the authors at a Langeoog seminar of
SFB/TR12 Symmetries and Universality in Mesoscopic Systems to a mixed audience 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 …

A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York
University This book is a concise and self-contained introduction of recent techniques to …

Random matrix theory is a wide and growing field with a variety of concepts, results, and
techniques and a vast range of applications in mathematics and the related sciences. The …

We consider the ensemble of adjacency matrices of Erdős–Rényi random graphs, that is,
graphs on N vertices where every edge is chosen independently and with probability …

Consider N× N Hermitian or symmetric random matrices H with independent entries, where
the distribution of the (i, j) matrix element is given by the probability measure νij with zero …

Abstract Consider N× N Hermitian or symmetric random matrices H where the distribution of
the (i, j) matrix element is given by a probability measure ν ij with a subexponential decay …

We prove that the largest eigenvalues of the beta ensembles of random matrix theory
converge in distribution to the low-lying eigenvalues of the random Schrödinger operator …

Abstract We prove the Wigner‐Dyson‐Mehta conjecture at fixed energy in the bulk of the
spectrum for generalized symmetric and Hermitian Wigner matrices. Previous results …