5 problems

Let $M$ be a channel and $T_b$ the $b$-ary tree. For $n$ and $m$, let $\sigma_{n,m}$ be obtained from the level-$n$ configuration $\sigma_n$ by applying $M^m$ independently to each…

Potts monotonicity conjecture. If reconstruction is solvable for $M_1$, then it is also solvable for $M_2$.

Consider the symmetric Potts channel $M$ on $q\geq 3$ symbols, with $b$-ary tree branching factor $b$ and second eigenvalue $\lambda_2(M)$. Potts-model below-bound conjecture. Ther…

Let $M$ be a channel with second eigenvalue $\lambda_2(M)$, and let $T_b$ be the $b$-ary tree. The reconstruction problem is census-solvable when the root can be reconstructed from…

Mézard–Montanari's conjecture. If $q\leq 4$ and $d<d_{\max}$, then there is reconstruction if and only if