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arxiv: math-ph/0112017 · v3 · submitted 2001-12-10 · 🧮 math-ph · cond-mat· hep-th· math.MP· nlin.CD

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Wishart and Anti-Wishart random matrices

Romuald A. Janik , Maciej A. Nowak
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classification 🧮 math-ph cond-mathep-thmath.MPnlin.CD
keywords matricesrandominformationmatrixredundantrepresentationwishartwishart-type
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We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices $A^\dagger A$, 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.

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