**March 19, 2019 at 2:30 p.m. in Yost 306**

**Thesis Title:** *On Truncations of Haar Distributed Random Matrices*

**Thesis Advisor:** Dr. Elizabeth Meckes

**Thesis Abstract**

The main focus of this dissertation is truncations, that is, principal submatrices of an n x n random Haar distributed matrix. We show that a p x q truncation of a random orthogonal matrix is close (in total variation distance) to a p x q matrix of independent identically distributed Gaussian random variables when pq = o(n). We also consider the limiting spectral measure of square truncations of a random unitary matrix and develop some nonasymptotic results describing the ensemble of eigenvalues of the truncations.