Hypergraph coloring up to condensation

Abstract

Improving a result of Dyer, Frieze and Greenhill [Journal of Combinatorial Theory, Series B, 2015], we determine the $q$-colorability threshold in random $k$-uniform hypergraphs up to an additive error of $\\ln 2+\\varepsilon_q$, where $\\lim_{q\\to\\infty}\\varepsilon_q=0$. The new lower bound on the threshold matches the condensation phase transition predicted by statistical physics considerations [Krzakala et al., PNAS 2007].