**Signal and Noise in a Gaussian Correlation Matrix**

Jerzy Jurkiewicz

Marian Smoluchowski Institute of Physics

Jagellonian University

**Abstract:**

Using random matrix technique it is possible to determine an
exact relation between the eigenvalue spectrum of the covariance matrix and of
its estimator. This relation can be used in practice to compute eigenvalue
invariants of the covariance (correlation) matrix. Results can be applied in
various problems where one experimentally estimates correlations in a system
with many degrees of freedom, in particular in quantitative finance and other
applications of multivariate statistics.