5 problems

Let $\Omega_n$ be the set of doubly-stochastic $n\times n$ matrices, and define … The authors exhibit doubly-stochastic matrices $A$ for which…

Let $\mathsf{N}$ be a double-edge normal factor graph (DE-NFG). For each integer $M\geq 1$, let $Z_{\mathrm{B},M}(\mathsf{N})$ denote the degree-$M$ Bethe partition function, defin…

Navin-type conjecture. It holds that

Cluster Bethe-approximation conjecture. The restricted measure $\mu_{\ell,n}$ is Bethe approximated by the message set $\{\nu^*_{i\to j}\}$.

Bethe-state decomposition conjecture. A large class of models, including for instance those examples, decomposes into convex combinations of Bethe states.