10 problems

Under Assumption … sigma^Y{i,j}geq sigma^X{i,j}geq 0 … operatorname{Cov}(log SN({mathbf G}),pi({mathbf G})pj({mathbf G}))leq 0. … ; its resolution is not indicated in the supplied…

Let $\Omega_0$ and $\Omega_1$ be open, bounded, centrally symmetric subsets of $\mathbb{R}^n$, and let $t\in[0,1]$. Write … The Gaussian torsional rigidity of a set $\Omega$ is den…

Let $d>0$ and let $K,T\subseteq \mathbb R^d$ be origin-symmetric convex sets, and let $\gamma_d$ denote the usual Gaussian probability measure. Teheranchi's strong Gaussian correla…

Let $X_1,\dots, X_n$ be zero-mean jointly Gaussian real random variables, and let $s_1,\dots, s_n, t_1,\dots, t_n \in [0,\infty)\cup \{\infty\}$. Teheranchi's strong Gaussian corre…

Let $n\in\mathbb{N}$ and let $p_1,\dots,p_n\in 2\mathbb{N}$. For a real centered Gaussian vector $(X_1,\dots,X_n)$, the statement $\mathbf{GPI}_n(p_1,\dots,p_n)$ means … with equal…

Let $m_1,m_2,m_3\in\mathbb{N}$, and let $(X_1,X_2,X_3)$ be a centered Gaussian random vector. Three-dimensional Gaussian product inequality conjecture. … The equality sign is asser…

Let $n\ge 3$, let $m_1,\dots,m_n\in\mathbb{N}$, and let $U_1,\dots,U_n$ be independent standard Gaussian random variables. Define the polynomial $H$ on $\mathbb{R}^{n(n-1)/2}$ by ……

Combinatorial positivity conjecture.

Let $d\geq 2$, let $(G_1,\ldots,G_d)$ be a $d$-dimensional real-valued centered Gaussian vector, and let $m\geq 1$ be an integer. Gaussian Product Conjecture. One has … This is an…

Let $d\geq 2$, let $x_1,\ldots,x_d$ be unit vectors in $\mathbb{R}^d$, and let $v$ be a unit vector in $\mathbb{R}^d$. The $d$th linear polarization constant $c_d(\mathcal{H})$ is…