4 problems

Cohen's one-sided max conjecture. Whenever

Let $X$ and $Y$ be centered Gaussian vectors with covariance matrices $\Sigma_X$ and $\Sigma_Y$, respectively. Write $\Sigma_Y\succeq\Sigma_X$ for the Loewner ordering, and let $f$…

Universal Rademacher-Gaussian comparison conjecture. The comparison in (R-G) continues to hold with a universal constant for every $d$ and every $n$ vectors in $\mathbb{R}^d$.

Let $\mathbf{X}=(X_1,\ldots,X_d)$ and $\mathbf{Y}=(Y_1,\ldots,Y_d)$ be $d$-dimensional Gaussian vectors with common mean $\bm{\mu}=(\mu_1,\ldots,\mu_d)$ and covariance matrices…