Wishart and Anti-Wishart random matrices
Mathematical Physics
2008-11-26 v3 Condensed Matter
High Energy Physics - Theory
math.MP
Chaotic Dynamics
Abstract
We provide a compact exact representation for the distribution of the matrix elements of the Wishart-type random matrices , for any finite number of rows and columns of , 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.
Cite
@article{arxiv.math-ph/0112017,
title = {Wishart and Anti-Wishart random matrices},
author = {Romuald A. Janik and Maciej A. Nowak},
journal= {arXiv preprint arXiv:math-ph/0112017},
year = {2008}
}
Comments
11 pages; v2: references updated + some clarifications added; v3: version to appear in J. Phys. A, Special Issue on Random Matrix Theory