N. Williams

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math.PR2019

Partial linear eigenvalue statistics for non-Hermitian random matrices

Sean O'Rourke, Noah Williams

For an $n \times n$ independent-entry random matrix $X_{n}$ with eigenvalues $λ_{1}, \dots, λ_{n}$ , the seminal work of Rider and Silverstein asserts that the fluctuations of the linear…

math.PR2018

On the local pairing behavior of critical points and roots of random polynomials

Sean O'Rourke, Noah Williams

We study the pairing between zeros and critical points of the polynomial $p_{n} (z) = \prod_{j = 1}^{n} (z - X_{j})$ , whose roots $X_{1}, \dots, X_{n}$ are complex-valued random variables. Under…