The field of random matrix theory has seen an explosion of activity in recent years, with
connections to many areas of mathematics and physics. However, this makes the current …

The Kaczmarz method for solving linear systems of equations is an iterative algorithm that
has found many applications ranging from computer tomography to digital signal …

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 …

Given an n× n complex matrix A, let A (x, y):= 1 n|{1 ≤ i ≤ n, Re i ≤ x, Im i ≤ y\}| be the
empirical spectral distribution (ESD) of its eigenvalues λ i∈ ℂ, i= 1,…, n. We consider the …

This book gathers threads that have evolved across different mathematical disciplines into
seamless narrative. It deals with condition as a main aspect in the understanding of the …

We prove two basic conjectures on the distribution of the smallest singular value of random
n× n matrices with independent entries. Under minimal moment assumptions, we show that …

These expository notes are centered around the circular law theorem, which states that the
empirical spectral distribution of an× n random matrix with iid entries of variance 1/n tends to …

Recent progress in combinatorial random matrix theory Page 1 Probability Surveys Vol. 18 (2021)
179–200 ISSN: 1549-5787 https://doi.org/10.1214/20-PS346 Recent progress in combinatorial …

Let x be a complex random variable with mean zero and bounded variance σ2. Let Nn be a
random matrix of order n with entries being iid copies of x. Let λ1,…, λn be the eigenvalues …

Singularity of random Bernoulli matrices Page 1 Annals of Mathematics 191 (2020), 593–634
https://doi.org/10.4007/annals.2020.191.2.6 Singularity of random Bernoulli matrices By …