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.

9 pages, 3 figures, references added

References in corpus (2)

• Information transfer through disordered media by diffuse waves
• Non-extensive RMT Approach to Mixed Regular-Chaotic Dynamics

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