title: Spectral properties of empirical covariance matrices for data with power-law tails.
abstract: 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.
authors.affiliation: 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
authors.forename: Zdzisław
authors.initials: Z
authors.lastname: Burda
authors.forename: Andrzej T
authors.initials: AT
authors.lastname: Görlich
authors.forename: Bartłomiej
authors.initials: B
authors.lastname: Wacław