10 problems

Let $(X_k)$ be independent copies of a nondegenerate nonnegative random variable, let $S_n=X_1+\cdots+X_n$, and set $Z_n=\sum_{k=1}^n e^{\imath S_k}$. For $p>0$, write…

Let $X\sim f_X$ and $Z\sim f_Z$ be independent random variables, where $f_X$ and $f_Z$ are densities with cumulative distribution functions $F_X$ and $F_Z$, respectively. Integral…

Let $L$ denote the set of all real random variables $X$ with a log-concave probability density function such that $EX=0$ and $EX^2=1$. Let $Y$ have the standard exponential distrib…

The properties CNA+, JNRD+ and h-NLC+ are stronger versions of CNA, JNRD and hereditary NLC, respectively, requiring the corresponding property after every imposition of an externa…

Let $q>0$ be real, let $a_1,\dots,a_n$ be non-negative real numbers satisfying … and let $X_1,\dots,X_n$ be independent identically distributed standard exponential random variable…

Let $G$ be a graph, let $A\subset G$, and let $0,b\in G$ be vertices. The uniform continuity conjecture. For every $\varepsilon>0$ there exists $\delta>0$ such that, whenever … and…

Let $G$ be a finite graph with arbitrary probabilities on its edges. Let $0,b\in G$ be vertices and let $A\subset G$ be a set of vertices. The pre-FKG conjecture. … This is a forma…

Let $G$ be a finite graph with arbitrary probabilities on its edges. Let $0,b\in G$ be vertices and let $A\subset G$ be a set of vertices. The post-FKG conjecture. … This is an FKG…

Let $p\in\mathbb{N}$, let $\alpha\in(p-1,\infty)$, and let $\Sigma\in\mathcal{S}_{++}^p$. Let $\mathfrak{X}\sim\mathcal{W}_p(\alpha,\Sigma)$ be a $p\times p$ Wishart random matrix,…

Latała's moment conjecture. There exists a universal constant $C$ such that, for every log-concave vector $X$ with values in a finite-dimensional normed space $(F,\|\ \|)$ and ever…