5 problems

Let $\mathcal{C}$ be the set of bivariate copulas, equivalently the set of joint laws of random variables $U,V\sim\mathcal{U}(0,1)$. Define Spearman's rho and Spearman's footrule b…

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 $X$ be a random variable on $\mathbb{S}^m$ whose local Fréchet mean is smeary, as in the curse of dimensionality theorem, and let the corresponding local Fréchet means be those…

For each $n,k$, consider left Gog and GOGAm trapezoids of shape $(n,k)$, and let $X_{1,1}=l$ denote their bottom entry. Refined left Gog–GOGAm conjecture. For each $n,k,l$, the…

For Gog, Magog and GOGAm triangles, define the statistics $\alpha$, $\beta$, and $\gamma$ as in the paper; in particular, $\alpha_{\mathrm{Gog}}(X)$ counts indices $k$ with…