A fundamental rule of statistics has been hiding a secret connection to five-dimensional physics and the behavior of subatomic particles.
The Gaussian correlation inequality is a basic truth about how probabilities overlap in bell curves. This new work reinterprets a famous proof of that rule using the heavy machinery of supersymmetry. It maps the problem from a standard space into a five-dimensional realm with three dimensions for normal matter and two for fermionic particles. By reducing these five dimensions down to one, the proof becomes much clearer. This connects the everyday math used in finance and engineering directly to the cutting edge of theoretical physics.
Royen's proof of the Gaussian correlation inequality as a supersymmetric dimensional reduction
arXiv · 2605.00533
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 generaliz