A note on the exact simulation of a random eigenvalue of a GUE matrix

Luc Devroye; Jad Hamdan

doi:10.1016/j.spl.2026.110736

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arXiv · 2304.03741

A note on the exact simulation of a random eigenvalue of a GUE matrix

Luc Devroye·Jad Hamdan

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Abstract

We develop a simple algorithm to generate random variables described by densities equaling squared Hermite functions. As an application, we show how to generate a randomly chosen eigenvalue of a matrix from the Gaussian Unitary Ensemble ({\textsc{gue}}) in sub-linear expected time.

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Luc Devroye, Jad Hamdan. 2023-04-07. A note on the exact simulation of a random eigenvalue of a GUE matrix. https://doi.org/10.1016/j.spl.2026.110736

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