Sean O’Rourke

activity

20112022

most citedControllability of random systems: Universality and minimal controllability

11 citations · 11 across the 4 of their papers we have counts for

collaborators

12 papers

math.PR2022

Spectrum of Lévy-Khintchine Random Laplacian Matrices

Andrew Campbell, Sean O'Rourke

We consider the spectrum of random Laplacian matrices of the form $L_{n} = A_{n} - D_{n}$ where $A_{n}$ is a real symmetric random matrix and $D_{n}$ is a diagonal matrix whose entries are equal…

math.PR2020

Eigenvectors and controllability of non-Hermitian random matrices and directed graphs

Kyle Luh, Sean O'Rourke

We study the eigenvectors and eigenvalues of random matrices with iid entries. Let $N$ be a random matrix with iid entries which have symmetric distribution. For each unit eigenvec…

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.AP2019

A Nonlocal Transport Equation Modeling Complex Roots of Polynomials under Differentiation

Sean O'Rourke, Stefan Steinerberger

Let $p_{n} : C \to C$ be a random complex polynomial whose roots are sampled i.i.d. from a radial distribution $u (r) r d r$ in the complex plane. A natural que…

math.PR2019

Sums of random polynomials with independent roots

Sean O'Rourke, Tulasi Ram Reddy

We consider the zeros of the sum of independent random polynomials as their degrees tend to infinity. Namely, let $p$ and $q$ be two independent random polynomials of degree $n$ , w…

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…