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

2024/12/14 by Terence Tao, Tao, Terence · 1 citation
Mathematics · #Spectral Theory in Mathematical Physics #Differential Equations and Boundary Problems #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2412.10889

Abstract

We obtain bounds on the distribution of normalized gaps of eigenvalues of N × N GUE matrix in the bulk, that do not lose logarithmic factors of N in the limit N → ∞. 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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• Optimal transport, determinantal point processes and the Bergman kernel

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