Vandermonde Squared: The Bridge Between GUE Eigenvalues and Zeta Zeros — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: The search results converge on the deep connection between the Vandermonde determinant (squared) and the eigenvalue density of Gaussian Unitary Ensemble (GUE) matrices, which is the same structure governing the statistical distribution of Riemann zeta zeros. | MATH: The GUE eigenvalue joint density is \( P(\lambda_1,\dots,\lambda_N) \propto \prod_{i \lambda_2 > \dots > \lambda_N \), where the density is supported. The Wigner semicircle law emerges as \( N \to \infty \): \( \rho(\lambda) = \frac{1}{2\pi}\sqrt{4 - \lambda^2} \) for \( \lambda \in [-2,2] \). | CONNECTION: The \( A_{N-1} \) root system is the symmetry of the \( N \)-simplex — its Weyl chamber volume is exactly the Vandermonde product. The squared Vandermonde is the Jacobian of the diagonaliza 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: W7212386722
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