Recent developments in non-asymptotic theory of random matrices

TL;DR

This paper surveys recent advances in the non-asymptotic analysis of random matrices, focusing on spectral properties with high probability and their applications in high-dimensional problems and algorithm analysis.

Contribution

It compiles recent results and techniques for explicit probability bounds in the non-asymptotic theory of random matrices.

Findings

Summarizes key recent results in non-asymptotic random matrix theory.

Highlights techniques for deriving explicit probability bounds.

Discusses applications in high-dimensional convexity and algorithms.

Abstract

Non-asymptotic theory of random matrices strives to investigate the spectral properties of random matrices, which are valid with high probability for matrices of a large fixed size. Results obtained in this framework find their applications in high-dimensional convexity, analysis of convergence of algorithms, as well as in random matrix theory itself. In these notes we survey some recent results in this area and describe the techniques aimed for obtaining explicit probability bounds.