English

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 AAA^\dagger A, for any finite number of rows and columns of AA, 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

R2 v1 2026-07-22T16:20:56.133Z