4 problems

Let $G$ be a random $\Delta$-regular bipartite graph on $2n$ vertices, let $\mu_{G,q;\beta}$ be the anti-ferromagnetic $q$-state Potts Gibbs distribution, and let an FPAUS mean a f…

Let $k$ be the clause size and let $d$ denote the relevant density parameter for the uniform $k$-SAT distribution. Sharp sampling-threshold conjecture. It is conjectured that the s…

Let $\mu$ be a distribution on configurations of a graph, and suppose it satisfies strong spatial mixing (SSM): the total variation influence of boundary pinnings on a vertex's mar…

Critical-fugacity tightness conjecture. The bound $\lambda_c(d)$ on the fugacity is tight in the sense that, for $\lambda>\lambda_c(d)$, efficient approximate sampling may still be…