N. Williams

activity

20162023

most citedPairing between zeros and critical points of random polynomials with independent roots

4 citations · 7 across the 4 of their papers we have counts for

collaborators

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3 papers · 1 filter

math.PR2019★ 1 cited

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★ 2 cited

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…

math.PR2016★ 4 cited

Pairing between zeros and critical points of random polynomials with independent roots

Sean O'Rourke, Noah Williams

Let $p_{n}$ be a random, degree $n$ polynomial whose roots are chosen independently according to the probability measure $μ$ on the complex plane. For a deterministic point $ξ$ lying…