5 problems

Existence conjecture. There exists a tropical Fermat–Weber point

Phase-transition conjecture. If $A(\beta_i)\leq 0$, then

Utility-function conjecture. $\mathcal{U}$ is non-increasing and convex in $t$. Numerical evidence supports this stronger claim, which would describe not only when the information/…

Let $F_t$ be the limiting spectral distribution of the noisy sample covariance matrix at noise power $t\geq 0$, and let $N(t)$ denote the number of connected components of its supp…

Let $n,d\to\infty$ with $n/d\to c>0$ and $n_\ell/n\to p_\ell$ for $\ell\in\{1,\dots,L\}$. Let $A$ and $\beta_i$ be the quantities defined in the paper, and let $\hat{u}_i$ be the…