3 problems

Let $\gamma_n$ be the standard Gaussian measure on $\mathbb{R}^n$, defined by … For $\lambda\in(0,1)$ and sets $A,B\subset\mathbb{R}^n$, write…

Let $\gamma_n$ be the Gaussian probability measure on $\mathbb{R}^n$, and let $K_1$ and $K_2$ be symmetric convex bodies in $\mathbb{R}^n$. The Gaussian Correlation Conjecture. The…

The perturbed-metric conjecture. For every $0<s<1$, there exist constants $C_s,c_s>0$ such that, whenever $\varepsilon(A)<e^{-1/\rho}$,