Year: 2026
Type: preprint
Abstract: We define a rank-two extension $\mathcal{H}^{(2)}$ of the spherical $\mathcal{H}$-transform, together with its associated transform $\mathcal{R}^{(2)}$. For sums, both transforms are additive. The transform $\mathcal{R}^{(2)}$ yields a $4\times4$ formula for the average product of two hermitized resolvents, and hence for off-diagonal eigenvector overlaps, recovering the Ginibre, elliptic, and bi-invariant formulas. We also treat correlated pairs of matrices, and obtain overlaps between their eigenvectors or singular vectors.
Source: arXiv (Cornell University)
Author: Bousseyroux, Pierre
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214025007
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