Hypergraph coloring up to condensation

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 ln2+epsilon q, where limq ->infinity epsilon q=0. The new lower bound on the threshold matches the "condensation phase transition" predicted by statistical physics considerations [Krzakala et al., PNAS 2007].