Spectral properties of empirical covariance matrices for data with power-law tails.
We present an analytic method for calculating spectral densities of empirical covariance matrices for correlated data. In this approach the data is represented as a rectangular random matrix whose columns correspond to sampled states of the system. The method is applicable to a class of random matrices with radial measures including those with heavy (power-law) tails in the probability distribution. As an example we apply it to a multivariate Student distribution.
Burda
Zdzisław
Z
Mark Kac Center for Complex Systems Research and Marian Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Krakow, Poland. burda@th.if.uj.edu.pl
Görlich
Andrzej T
AT
Wacław
Bartłomiej
B