6 problems

Consider a stochastic block model in the sparse regime where the average degree is of constant order, and let the Kesten–Stigum threshold be $d_{\mathrm{KS}}=\lambda^{-2}$. ACKZ's…

Let $d$ be the average degree and let $d_{\tiny\textsf{\textup{KS}}}:=\lambda^{-2}$ denote the Kesten–Stigum threshold. DKMZ's conjecture. Above the Kesten–Stigum threshold,…

Chodrow et al.'s conjecture. Weak recovery is possible above the Kesten–Stigum threshold. The conjecture concerns the natural extension of the uniform-hypergraph threshold to hyper…

Consider the symmetric stochastic block model with $q=4$ communities, parameters $d$ and $\lambda$, and Kesten–Stigum threshold $d\lambda^2=1$. Tightness means that weak recovery i…

Consider the symmetric stochastic block model with $q=4$ communities, parameters $d$ and $\lambda$, and Kesten–Stigum threshold $d\lambda^2=1$. Tightness means that this threshold…

Let $r\ge 2$ and consider the $r$-uniform hypergraph stochastic block model with two symmetric communities, expected degree parameter $d$ and strength parameter $\lambda$. Weak rec…