De Finetti-Style Results for Wishart Matrices: Combinatorial Structure and Phase Transitions

Matthew Brennan, Guy Bresler, Brice Huang

A recent line of work has studied the relationship between the Wishart matrix $X^{\top }X$, where $X\in {\mathbb{R}}^{d\times n}$ has i.i.d. standard Gaussian entries, and the correspo…