Vandermonde Kernel Unifies GUE and Zeta Zeros via Weyl Chambers — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The search results converge on the deep structural identity between the Vandermonde determinant (squared) and the eigenvalue density of Gaussian Unitary Ensemble (GUE) random matrices, which is the same mathematical kernel governing the statistical distribution of Riemann zeta zeros — a connection explicitly bridged by the Weyl chamber volume of the A_{N-1} root system. MATH: - GUE eigenvalue joint density: \( p(\lambda_1,\dots,\lambda_N) \propto \prod_{i \lambda_2 > \dots > \lambda_N \), exactly the ordered eigenvalue space. - Zeta zeros statistics: Montgomery–Odlyzko law — the pair correlation of zeta zeros matches GUE eigenvalue spacing, with density \( 1 - \left(\frac{\si Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7212429332
Cites:
Cited by:
Related to: