The Ball-Nayar-Tkocz conjecture asserts that, for independent real random variables $X,Y$ with a common log-concave density, the function $t\mapsto h(\sqrt tX+\sqrt{1-t}Y)$ is concave on $[0,1]$. Gaussian distributions have this property. We construct strongly log-concave counterexamples arbitrarily close to the Gaussi...
Random geometric graph detection asks whether a graph generated from $n$ independent uniform points on $S^{d-1}$, with edge probabilities depending on inner products, can be distinguished from an Erdos-Renyi graph of the same edge density using only its adjacency matrix. Mao, Wu, and Xu conjectured that the cubic trace...
Given a finite preorder $\tau$, we study how its order relation determines the $h^*$-polynomial of the associated polar preorder polytope. Let $\mathcal R_{\tau}^{\vee}$ be the convex hull of the negative standard basis vectors and the indicator vectors of nonempty order ideals, and write $h_\tau^*(t)=h^*(\mathcal R_{\...
It is studied whether an observed graph can distinguish a random graph generated by latent geometry from one with independent edges, which is an Erdős–Rényi graph with the same edge density.
Cong-Ying Luo· 0 citations
We use cookies to run the site and, with your consent, for analytics and to show ads.
See our Cookie Policy.
