David Renfrew

On finite rank deformations of Wigner matrices

We study the distribution of the outliers in the spectrum of finite rank deformations of Wigner random matrices under the assumption that the absolute values of the off-diagonal matrix entries have uniformly bounded fifth moment and the abso- lute values of the diagonal entries have uniformly bounded third moment. Using our recent results on the fluctuation of resolvent entries (On fluctuations of matrix entries of regular functions of Wigner matrices with non-identically distributed entries, Unpub- lished manuscript; Fluctuations of matrix entries of regular functions of Wigner matrices, Unpublished manuscript) and ideas from (Fluctuations of the extreme eigenvalues of finite rank deformations of random matrices, Unpublished manuscript), we extend the results by Capitaine, Donati-Martin, and Feral (Ann. Probab. 37 (2009) 1–47; Ann. Inst. Henri Poincare Probab. Stat. 48 (2012) 107–133).

Products of Independent Elliptic Random Matrices

For fixed

On Finite Rank Deformations of Wigner Matrices II: Delocalized Perturbations

m > 1

Low-dimensional dynamics of structured random networks

m>1, we study the product of

Low rank perturbations of large elliptic random matrices

m

Central Limit Theorem for Linear Eigenvalue Statistics of Elliptic Random Matrices

m independent