3 papers
math.PR2026
An asymptotic refinement of the Gauss-Lucas Theorem for random polynomials with i.i.d. roots
Sean O'Rourke, Noah Williams
If 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.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 is an random matrix with independent and identically distrib…
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…