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On the distribution of eigenvalues of GUE and its minors at fixed index
Terence Tao · 2024-12-15 · via math.PR updates on arXiv.org

We obtain bounds on the distribution of normalized gaps of eigenvalues of $N \times N$ GUE matrix in the bulk, that do not lose logarithmic factors of $N$ in the limit $N \to \infty$. As an application, we obtain fixed index universality results for the GUE minor process, which in turn are useful for establishing limiting results for random hives with GUE boundary data.

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