4 problems

Let $\mathbf{W}^{(n)}=\mathrm{W}_2^2(\hat\mu^{1,(n)},\hat\nu^{1,(n)})$ be the squared Wasserstein distance between two empirical samples of size $n$ from the standard normal distri…

Best-fit Stiefel tropical linear space conjecture. As $\sigma\to0$, the quantity

Monotonicity conjecture. The expectation above monotonically decreases with $k$. Consequently, as $\sigma\to0$, the hyperplane that best fits $X$ converges to $H_0$, meaning that t…

Cantelli's conjecture. The random variable $X+\varphi(X)\cdot Y$ has a Gaussian distribution if and only if $\varphi$ is constant.