5 problems

Let $x\in \mathcal{S}^{2}$ and, for $t\in \mathbb{R}$, let $\mathcal{L}_{l;x}^{t}$ denote the random length of the unique component of $f_l^{-1}(t)$ that contains $x$ inside, or…

Let $(X,Y)$ be bivariate normal random variables, and write $\varrho(X,Y)=\varrho$ for their correlation. The bivariate normal earth mover's correlation conjecture. One has … The p…

Let $V^{(n)}_{a}(\alpha,0)$ and $V^{(n)}_{c}(\alpha)$ denote the anagenetic and cladogenetic contributions to the variance, and let $C^{(n)}_{a}(\alpha,0)$ and…

Let $G=(V,A)$ be a directed acyclic graph, and consider two arcs incident on a common node. Incident-arc range conjecture. The covariance between the two arcs takes values in the i…

Let $G=(V,A)$ be a directed acyclic graph, and consider two arcs that are incident on a common node. Let covariance and correlation refer to the corresponding arc-indicator random…