Wishart and Anti-Wishart random matrices

Abstract

We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices $A^{†}A$, for any finite number of rows and columns of $A$, without any large N approximations. In particular we treat the case when the Wishart-type random matrix contains redundant, non-random information, which is a new result. This representation is of interest for a procedure of reconstructing the redundant information hidden in Wishart matrices, with potential applications to numerous models based on biological, social and artificial intelligence networks.

11 pages; v2: references updated + some clarifications added; v3: version to appear in J. Phys. A, Special Issue on Random Matrix Theory

References in corpus (3)

• Extracting Hidden Information from Knowledge Networks
• Negative moments of characteristic polynomials of random matrices: Ingham-Siegel integral as an alternative to Hubbard-Stratonovich transformation
• On the Anti-Wishart distribution

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