Wishart and Anti-Wishart random matrices

TL;DR

This paper derives an exact, finite-size distribution for Wishart-type matrices, including cases with redundant information, aiding in reconstructing hidden data in complex network models.

Contribution

It provides a novel exact representation for Wishart matrices with redundant information, extending beyond large N approximations.

Findings

Exact distribution formula for Wishart matrices with finite size.

Inclusion of cases with non-random, redundant data.

Potential applications in biological, social, and AI network models.

Abstract

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.