3 problems

Let ${\bm{\tau}}\in S_n^D$, and let $\nabla({\bm{\tau}};\eta)$ be the nonnegative quantity whose vanishing characterizes the relevant compatible configurations. For a permutation o…

Let $A\in(\mathbb{R}^N)^{\otimes p}$ have independent entries distributed as $\mathcal{N}(0,N^{-(p-1)})$, and let $\mathcal{B}_N\subset\mathcal{H}_N$ denote the binary and Hilbert-…

Hilbert-cube OGP conjecture. For every even $p\geq4$, there exist $\mu>0$ and $0<\nu_1<\nu_2<1$ such that $\mathcal{A}$ satisfies the OGP with domain $\mathcal{S}_N=\mathcal{H}_N$,…