Distances between Random Orthogonal Matrices and Independent Normals

Tiefeng Jiang, Yutao Ma

Let ${\Gamma }_n$ be an $n\times n$ Haar-invariant orthogonal matrix. Let $Z_n$ be the $p\times q$ upper-left submatrix of ${\Gamma }_n,$ where $p=p_n$ and $q=q_n$ are two positive integers. Let…