Sean O’Rourke

activity

20092026

most citedGaussian Fluctuations of Eigenvalues in Wigner Random Matrices

58 citations · 206 across the 36 of their papers we have counts for

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38 papers · 1 filter

math.PR2026

Universality for the extreme eigenvalues of Laplacian random matrices

Andrew Campbell, Kyle Luh, Sean O'Rourke

We study the eigenvalues of the random Laplacian matrix $D - A$ , where $A$ is a Wigner matrix with sub-Gaussian entries and the diagonal matrix $D$ contains the row sums of $A$ . Ou…

math.PR2026

Limiting spectral distribution for the adjacency matrix of the Watts-Strogatz random graph

Grégoire Meunier, Sean O'Rourke

The Watts-Strogatz random graph model on $n$ vertices with parameters $K$ (a positive even integer) and $p \in [0, 1]$ is constructed in two steps. First, one starts with a ring la…

math.PR2026

Real roots of non-centered random polynomials

Yen Q. Do, Nhan D. V. Nguyen, Sean O'Rourke

We study the fluctuations of the number of real roots of random polynomials with independent, nonzero-mean coefficients. Such non-centered ensembles arise naturally in signal-plus-…

math.PR2023

Spectrum of Laplacian matrices associated with large random elliptic matrices

Sean O'Rourke, Zhi Yin, Ping Zhong

A Laplacian matrix is a square matrix whose row sums are zero. We study the limiting eigenvalue distribution of a Laplacian matrix formed by taking a random elliptic matrix and sub…

math.PR2023

The fractional free convolution of $R$ -diagonal elements and random polynomials under repeated differentiation

Andrew Campbell, Sean O'Rourke, David Renfrew

We extend the free convolution of Brown measures of $R$ -diagonal elements introduced by Kösters and Tikhomirov [Probab. Math. Statist. 38 (2018), no. 2, 359--384] to fractional pow…

math.PR2022★ 1 cited

Extreme eigenvalues of Laplacian random matrices with Gaussian entries

Andrew Campbell, Kyle Luh, Sean O'Rourke +2

A Laplacian matrix is a real symmetric matrix whose row and column sums are zero. We investigate the limiting distribution of the largest eigenvalues of a Laplacian random matrix w…

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.PR2021

Sums of random polynomials with differing degrees

Isabelle Kraus, Marcus Michelen, Sean O'Rourke

Let $μ$ and $ν$ be probability measures in the complex plane, and let $p$ and $q$ be independent random polynomials of degree $n$ , whose roots are chosen independently from $μ$ and…

math.PR2021

Quantitative results for banded Toeplitz matrices subject to random and deterministic perturbations

Sean O'Rourke, Philip Matchett Wood

We consider the eigenvalues of a fixed, non-normal matrix subject to a small additive perturbation. In particular, we consider the case when the fixed matrix is a banded Toeplitz m…

math.PR2020

Spectrum of Heavy-Tailed Elliptic Random Matrices

Andrew Campbell, Sean O'Rourke

An elliptic random matrix $X$ is a square matrix whose $(i, j)$ -entry $X_{ij}$ is independent of the rest of the entries except possibly $X_{j i}$ . Elliptic random matrices generaliz…

math.PR2020★ 3 cited

Circular Law for Random Block Band Matrices with Genuinely Sublinear Bandwidth

Vishesh Jain, Indrajit Jana, Kyle Luh +1

We prove the circular law for a class of non-Hermitian random block band matrices with genuinely sublinear bandwidth. Namely, we show there exists $τ \in (0, 1)$ so that if the bandw…

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★ 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.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★ 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.PR2018★ 1 cited

Eigenvector Delocalization for Non-Hermitian Random Matrices and Applications

Kyle Luh, Sean O'Rourke

Improving upon results of Rudelson and Vershynin, we establish delocalization bounds for eigenvectors of independent-entry random matrices. In particular, we show that with high pr…

math.PR2018

Gaussian fluctuations for linear eigenvalue statistics of products of independent iid random matrices

Natalie Coston, Sean O'Rourke

Consider the product $X = X_{1} \dots X_{m}$ of $m$ independent $n \times n$ iid random matrices. When $m$ is fixed and the dimension $n$ tends to infinity, we prove Gaussian limits…

math.PR2018

Random matrix products: Universality and least singular values

Phil Kopel, Sean O'Rourke, Van Vu

We establish, under a moment matching hypothesis, the local universality of the correlation functions associated with products of $M$ independent iid random matrices, as $M$ is fix…

math.PR2017

Outliers in the spectrum for products of independent random matrices

Natalie Coston, Sean O'Rourke, Philip Matchett Wood

For fixed positive integers m, we consider the product of m independent n by n random matrices with iid entries as in the limit as n tends to infinity. Under suitable assumptions o…

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…

math.PR2016★ 1 cited

Low-degree factors of random polynomials

Sean O'Rourke, Philip Matchett Wood

Motivated by the question of whether a random polynomial with integer coefficients is likely to be irreducible, we study the probability that a monic polynomial with integer coeffi…

math.PR2016★ 8 cited

Eigenvectors of random matrices: A survey

Sean O'Rourke, Van Vu, Ke Wang

Eigenvectors of large matrices (and graphs) play an essential role in combinatorics and theoretical computer science. The goal of this survey is to provide an up-to-date account on…

math.PR2015★ 5 cited

Spectra of nearly Hermitian random matrices

Sean O'Rourke, Philip Matchett Wood

We consider the eigenvalues and eigenvectors of matrices of the form M + P, where M is an n by n Wigner random matrix and P is an arbitrary n by n deterministic matrix with low ran…

math.PR2015★ 11 cited

Controllability of random systems: Universality and minimal controllability

Sean O'Rourke, Behrouz Touri

For a large class of random matrices $A$ and vectors $b$ , we show that linear systems formed from the pair $(A, b)$ are controllable with high probability. Despite the fact that min…

Universality for the extreme eigenvalues of Laplacian random matrices

Limiting spectral distribution for the adjacency matrix of the Watts-Strogatz random graph

Real roots of non-centered random polynomials

Spectrum of Laplacian matrices associated with large random elliptic matrices

The fractional free convolution of R-diagonal elements and random polynomials under repeated differentiation

Extreme eigenvalues of Laplacian random matrices with Gaussian entries

Spectrum of Lévy-Khintchine Random Laplacian Matrices

Sums of random polynomials with differing degrees

Quantitative results for banded Toeplitz matrices subject to random and deterministic perturbations

Spectrum of Heavy-Tailed Elliptic Random Matrices

Circular Law for Random Block Band Matrices with Genuinely Sublinear Bandwidth

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

Partial linear eigenvalue statistics for non-Hermitian random matrices

Sums of random polynomials with independent roots

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

Eigenvector Delocalization for Non-Hermitian Random Matrices and Applications

Gaussian fluctuations for linear eigenvalue statistics of products of independent iid random matrices

Random matrix products: Universality and least singular values

Outliers in the spectrum for products of independent random matrices

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

Low-degree factors of random polynomials

Eigenvectors of random matrices: A survey

Spectra of nearly Hermitian random matrices

Controllability of random systems: Universality and minimal controllability

The fractional free convolution of $R$ -diagonal elements and random polynomials under repeated differentiation