Wishart and Jacobi ensembles#

Covariance-type ensembles: Wishart’s original sample-covariance construction, the Marchenko-Pastur law, the Wachter law for Jacobi (MANOVA) ensembles, and Page’s conjecture for the average entanglement entropy of a random quantum state.

The Marchenko-Pastur Law

The Marchenko-Pastur Law

Page’s Conjecture: the Average Entanglement Entropy of a Random State

Page's Conjecture: the Average Entanglement Entropy of a Random State

The Wachter Law for Jacobi Ensembles

The Wachter Law for Jacobi Ensembles

Wishart’s Sample Covariance Matrix

Wishart's Sample Covariance Matrix