On the number of solutions in random hypergraph 2-colouring

We determine the limiting distribution of the logarithm of the number of satisfying assignments in the random $k$-uniform hypergraph 2-colouring problem in a certain density regime for all $k\ge 3$ . As a direct consequence we obtain that in this regime the random colouring model is contiguous wrt. the planted model, a result that helps simplifying the transfer of statements between these two models.