Royen's proof of the Gaussian correlation inequality as a supersymmetric dimensional reduction
Abstract
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 ℝ3|2 to ℝ1|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 ℝ3|2. The generalization to the half-integer multivariate Gamma case also follows naturally as a dimensional reduction from ℝk+2|2 to ℝk|0, and we derive an exact interpolation identity for general smooth test functions. This provides an example in which the supersymmetric localization method is applied to prove correlation inequalities with continuous interpolation.
Related
- Applications of Royen's Gaussian Correlation Inequality in high-dimensional testing
- Vacuum Structure of Maximally Supersymmetric Two-Dimensional Gauge Theories
- Scattering, bound states, and resonances in the one-dimensional Dirac equation via supersymmetric quantum mechanics
- Quantum Elliptic Cohomology From Four-Dimensional Minimal Supersymmetric Gauge Theories
- Towards Wedge Construction of Four-Dimensional Non-Supersymmetric Theories and Torsion Classes
BibTeX
@misc{huang2026royens,
title = {{Royen's proof of the Gaussian correlation inequality as a supersymmetric dimensional reduction}},
author = {Yichao Huang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.00533},
eprint = {2605.00533},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.00533},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Royen's proof of the Gaussian correlation inequality as a supersymmetric dimensional reduction
AU - Yichao Huang
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2605.00533
UR - https://arxiv.org/abs/2605.00533
AB - 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 ℝ^3|2 to 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 ℝ^3|2. The generalization to the half-integer multivariate Gamma case also follows naturally as a dimensional reduction from ℝ^k+2|2 to ℝ^k|0, and we derive an exact interpolation identity for general smooth test functions. This provides an example in which the supersymmetric localization method is applied to prove correlation inequalities with continuous interpolation.
ER -