On the distribution of eigenvalues of GUE and its minors at fixed index

Abstract

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.

arXiv comment43 pages, no figures