9 problems

Let $X=(X_1,\ldots,X_p)$ be a centered Gaussian vector with independent coordinates and variances $\lambda_1\ge\cdots\ge\lambda_p$. For a vector $z$, let…

Let $u=gamma$ be the Gaussian measure, let $L=-Deltagamma$ be the Ornstein–Uhlenbeck operator, and let $d(Omega)$ be the Gaussian Fraenkel asymmetry. The quantitative Gaussian Fab…

Vector-valued Borell inequality. If $0<\rho<1$ and

Let $K \subseteq \mathbb{R}^n$ be symmetric and convex, and let $v \in \mathbb{S}^{n-1}$ satisfy $\operatorname{Inf}_v[K] \leq \varepsilon$. A symmetric convex set $L$ can be compa…

Let $K$ be a symmetric convex set and suppose that the convex influence $\Inf_v[K]$ in every direction $v \in \mathbb{S}^{n-1}$ is at most $\delta$, with…

Let $n\geq 1$ and let $\gamma_n$ be the standard Gaussian probability measure on $\mathbb R^n$. For $t>0$, let $U_t$ denote the Gaussian diffusion operator, and for a measurable no…

A standard simplex partition of $\mathbb{R}^n$ is obtained from a regular simplex with center $P$ by taking, for each facet, the cone over that facet with common base point $P$. St…

Pisier inequality conjecture. If $X$ has Rademacher type $p>1$, then the factor $\log n$ can be replaced by a universal constant depending on the geometry of $X$.

Let $\operatorname{\mathcal{X}}_{2}^*$ be the set of real random variables of the form … where $c\in\mathbb{R}$, $\beta\in l_2(\mathbb{N})$, $\alpha\in l^2(\mathbb{N})$, and…