Correlations of the characteristic polynomials in the Gaussian Unitary Ensemble or a singular Hankel determinant
Abstract
We obtain large n asymptotics for products of powers of the absolute values of the characteristic polynomials in the Gaussian Unitary Ensemble of n× n matrices. Our results can also be interpreted as asymptotics of the determinant of a Hankel matrix whose symbol is supported on the real line and possesses power-like (Fisher-Hartwig) singularities.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.