A short proof of the Marchenko-Pastur theorem

TL;DR

This paper provides a simplified proof of the Marchenko-Pastur theorem applicable to random matrices with i.i.d. rows and complex dependence structures, extending the theorem's applicability.

Contribution

It introduces a straightforward modification of the Cauchy-Stieltjes resolvent method to prove the theorem under broader conditions.

Findings

Proof applicable to matrices with complex dependence within rows

Simplifies existing proof techniques

Extends the theorem's applicability to more general matrices

Abstract

We prove the Marchenko-Pastur theorem for random matrices with i.i.d. rows and a general dependence structure within the rows by a simple modification of the standard Cauchy-Stieltjes resolvent method.