7 problems

Diagonal stability conjecture. There exist positive constants $C_p>0$ such that, if $(r_k)$ is log-concave, then

Let $G$ be a standard Gaussian random variable, let $X_1,\ldots,X_n$ be independent identically distributed symmetric random variables with … and let $a_1,\ldots,a_n$ satisfy the n…

Third-moment stability conjecture. There exists a universal constant $C_3>0$ such that

Optimal fourth-moment deficit conjecture. For every $p\geq 3$,

Let $c(q)$ denote the optimal constant in the three-dimensional case, and let $c_{3,2}(q)$ be the constant obtained from two equal weights. For $-2<q<-1$, the value of the optimal…

Let $c(q)$ denote the optimal constant in the two-dimensional case, and let $c_{2,2}(q)$ be the constant obtained from two equal weights. For $-1<q<0$, the relevant bound is not kn…

Sharpness conjecture. The right condition in Theorem (1) should be