Universal Eigenvalue Statistics for Dynamically Defined Matrices

TL;DR

This paper demonstrates that Hermitian matrices generated from the doubling map exhibit spectral statistics consistent with the GUE universality class, bridging dynamical systems and random matrix theory.

Contribution

It establishes the universality of eigenvalue statistics for a new class of dynamically defined matrices derived from the doubling map.

Findings

Spectra of these matrices follow GUE statistics

Supports universality conjecture in random matrix theory

Connects dynamical systems with random matrix universality

Abstract

We consider dynamically defined Hermitian matrices generated from orbits of the doubling map. We prove that their spectra fall into the GUE universality class from random matrix theory.