Author

Sean O’Rourke

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Preprint Oct 2026

Universality for the extreme eigenvalues of Laplacian random matrices

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 $A$. Our main results show that the extreme eigenvalues of this model exhibit Poisson statistics; in particular, after the appropriate centering an...

A. Campbell, Kyle Luh, Sean O'Rourke · 0 citations

Preprint Jul 2026

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

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 lattice on $n$ vertices, where each vertex is connected to its $K/2$ nearest neighbors on each side. Each edge in turn is then independently r...

Grégoire Meunier, Sean O’Rourke · 0 citations