Royen's proof of the Gaussian correlation inequality as a supersymmetric dimensional reduction
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866914524290875392 |
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| author | Huang, Yichao |
| author_facet | Huang, Yichao |
| contents | We revisit Royen's proof of the Gaussian correlation inequality from a supersymmetric point of view. Many key elements in Royen's proof of this inequality have natural geometric interpretations in terms of supersymmetric dimensional reduction from $\mathbb{R}^{3|2}$ to $\mathbb{R}^{1|0}$. In particular, the auxiliary multivariate Gamma distributions appearing in Royen's Laplace-transform argument arise naturally as the body of a supersymmetric radial variable on $\mathbb{R}^{3|2}$. The generalization to the half-integer multivariate Gamma case also follows naturally as a dimensional reduction from $\mathbb{R}^{k+2|2}$ to $\mathbb{R}^{k|0}$. This provides an example in which the supersymmetric localization method is applied to prove correlation inequalities with continuous parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00533 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Royen's proof of the Gaussian correlation inequality as a supersymmetric dimensional reduction Huang, Yichao Probability Mathematical Physics Statistics Theory We revisit Royen's proof of the Gaussian correlation inequality from a supersymmetric point of view. Many key elements in Royen's proof of this inequality have natural geometric interpretations in terms of supersymmetric dimensional reduction from $\mathbb{R}^{3|2}$ to $\mathbb{R}^{1|0}$. In particular, the auxiliary multivariate Gamma distributions appearing in Royen's Laplace-transform argument arise naturally as the body of a supersymmetric radial variable on $\mathbb{R}^{3|2}$. The generalization to the half-integer multivariate Gamma case also follows naturally as a dimensional reduction from $\mathbb{R}^{k+2|2}$ to $\mathbb{R}^{k|0}$. This provides an example in which the supersymmetric localization method is applied to prove correlation inequalities with continuous parameters. |
| title | Royen's proof of the Gaussian correlation inequality as a supersymmetric dimensional reduction |
| topic | Probability Mathematical Physics Statistics Theory |
| url | https://arxiv.org/abs/2605.00533 |