Correlated Wishart Matrices and Critical Horizons

TL;DR

This paper presents a practical method for determining the eigenvalue spectrum of empirical correlation matrices using conformal maps and critical horizons, based on the Marčenko-Pastur equation, aiding in spectral analysis.

Contribution

It introduces a novel approach utilizing conformal maps at critical horizons to analyze the eigenvalue spectrum of correlation matrices, enhancing spectral determination methods.

Findings

Provides a practical method for spectrum determination

Utilizes conformal map analysis at critical horizons

Based on the Marčenko-Pastur equation

Abstract

We discuss a practical method to determine the eigenvalue spectrum of the empirical correlation matrix. The method is based on the analysis of the behavior of a conformal map at a critical horizon which is defined as a border line of the physical Riemann sheet of this map. The map is a convenient representation of the Mar\v{c}enko-Pastur equation.