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. 
Zdzislaw Burda, Andrzej Goerlich, Bartlomiej Waclaw