Spectral Density of Sparse Sample Covariance Matrices

Details Spectral Density of Sparse Sample Covariance Matrices Spectral Density of Sparse Sample Covariance Matrices

2006-12-22

arxiv.org/abs/cond-mat/0612584v2

J. Phys. A: Math. Theor. 40 (2007) 4973

Physics

Condensed Matter

Statistical Mechanics

22 pages, 4 figures, minor corrections made

Scientific paper

Applying the replica method of statistical mechanics, we evaluate the eigenvalue density of the large random matrix (sample covariance matrix) of the form $J = A^{\rm T} A$, where $A$ is an $M \times N$ real sparse random matrix. The difference from a dense random matrix is the most significant in the tail region of the spectrum. We compare the results of several approximation schemes, focusing on the behavior in the tail region.

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