Sean O’Rourke

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math.PR2026

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

GrÃ©goire 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.PR2024

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…