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| Main Author: | |
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| Format: | Recurso digital |
| Language: | English |
| Published: |
Zenodo
2026
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| Subjects: | |
| Online Access: | https://doi.org/10.5281/zenodo.18532134 |
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Table of Contents:
- <p>For Kullback–Leibler divergence between multivariate Gaussians, a sharp relaxed triangle inequality was recently obtained by Xiao et al. (arXiv:2602.02577v1, 2026). This paper develops an analogous extremal program for the Rényi divergence of order α = 1/2 in the one-dimensional Gaussian family. We derive a complete budget decomposition, prove an explicit closed-form optimum under a mirror-symmetry ansatz via a transcendental equation (S = 2 sinh(2s*)), establish that the supremum cannot be achieved at zero means, eliminate the plus-branch sector, and reduce the full mirror-symmetry conjecture to a single explicit Schur-concavity inequality. Extensions to general Rényi order α and to higher dimensions under commuting covariances are also provided.</p>