Bernoulli Random Matrices

TL;DR

This paper reviews recent advances in Random Matrix theory, focusing on the spectral properties and eigenvectors of Bernoulli matrices, highlighting key results and techniques developed over the past thirty years.

Contribution

It provides an overview of the current state of knowledge on Bernoulli matrices, emphasizing spectral and eigenvector properties in Random Matrix theory.

Findings

Spectral distribution of Bernoulli matrices is well-understood.

Eigenvector behavior has been characterized in recent studies.

New techniques have advanced the analysis of Bernoulli matrices.

Abstract

Random Matrix theory has become a field on its own with a breadth of new results, techniques, and ideas in the last thirty years. In these proceedings of the 8ECM 2021, I illustrate some of these advances by describing what is known about the spectrum and the eigenvectors of Bernoulli matrices.