Sean O'Rourke

activity

20232026

collaborators

5 papers

math.PR2026

Repeated differentiation of random polynomials with i.i.d. rotationally invariant roots

Sean O'Rourke

Let $p_{n}$ be a random polynomial of degree $n$ whose roots are independent and identically distributed according to a rotationally invariant probability measure $μ_{0}$ on the comple…

math.PR2025

The Limiting Spectral Distribution for Sparse Elliptic Random Matrices

Jackson Carpenter, Sean O'Rourke

This paper studies sparse elliptic random matrix models which generalize both the classical elliptic ensembles and sparse i.i.d. matrix models by incorporating correlated entries a…

math.PR2025

Gaps between Singular Values of Sample Covariance Matrices

Nicholas Christoffersen, Kyle Luh, Sean O'Rourke +1

We study the gaps between consecutive singular values of random rectangular matrices. Specifically, if $M$ is an $n \times p$ random matrix with independent and identically distrib…

math.PR2024

An asymptotic refinement of the Gauss-Lucas Theorem for random polynomials with i.i.d. roots

Sean O'Rourke, Noah Williams

If $p : C \to C$ is a non-constant polynomial, the Gauss--Lucas theorem asserts that its critical points are contained in the convex hull of its roots. We consider…

math.PR2023

On random polynomials with an intermediate number of real roots

Marcus Michelen, Sean O'Rourke

For each $α \in (0, 1)$ , we construct a bounded monotone deterministic sequence $(c_{k})_{k \geq 0}$ of real numbers so that the number of real roots of the random polynomial $f_n(z)…