7 problems

Let $\rho$) be the root of a tree, let $u$ denote the broadcast labeling on its vertices, and consider message-passing algorithms whose messages take values in an alphabet $\Sigma$…

Consider the model on a regular tree of degree parameter $d$, with broadcast parameter $\theta$, and a BMS survey channel $W$. Write $P_e(W)$ for the survey error probability, and…

Let $T$ be a regular tree or a Galton-Watson tree with Poisson offspring distribution, with root vertex $\rho$. Let $(T,\rho,\theta,W)$ denote the corresponding broadcast model wit…

Let $P_e(\delta)$ denote the optimal reconstruction error probability in the binary-tree broadcasting model, let $\delta_c$ be the critical channel parameter, and write…

Let $I(\delta)$ denote the mutual information in the binary-tree broadcasting model, let $\delta_c$ be the critical channel parameter, and write $\delta=\delta_c-\tau$ with…

Let $T$ be an infinite tree with root $\rho$. Assign the root a uniformly random label in $\{\pm1\}$ and propagate labels along edges, retaining the parent label with probability…

Let $T$ be an infinite tree with root $\rho$. In the two-state broadcast process, each vertex label $\tau_v\in\{\pm 1\}$ is generated by assigning the root a uniformly random label…