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Improving a result of Dyer, Frieze and Greenhill [Journal of CombinatorialTheory, 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 thresholdmatches the "condensation phase transition" predicted by statistical physicsconsiderations [Krzakala et al., PNAS 2007].

Hypergraph coloring up to condensation