Biomedical subjects

Zdzisław Burda

Publications and source records attributed to Zdzisław Burda.

3 recordsLinked to original sources

PubMed2006

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.

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PubMed2005

Spectral moments of correlated Wishart matrices.

We present an analytic method to determine the spectral properties of the covariance matrices constructed of correlated Wishart random matrices. The method gives, in the limit of large matrices, exact analytic relations between the spectral moments and the eigenvalue densities of the covariance matrices and their estimators. The results can be used in practice to extract the information about genuine correlations from the given experimental realization of random matrices.

Journal Article↗

PubMed2002

Free random Lévy matrices.

Using the theory of free random variables and the Coulomb gas analogy, we construct stable random matrix ensembles that are random matrix generalizations of the classical one-dimensional stable Lévy distributions. We show that the resolvents for the corresponding matrices obey transcendental equations in the large size limit. We solve these equations in a number of cases, and show that the eigenvalue distributions exhibit Lévy tails. For the analytically known Lévy measures we explicitly construct the density of states using the method of orthogonal polynomials. We show that the Lévy tail distributions are characterized by a different novel form of microscopic universality.

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