On the Number of Solutions in Random Hypergraph 2-Colouring
Keywords: Random Hypergraphs, 2-colouring, Small subgraph conditioning, Partition function, Limiting distribution
AbstractWe 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.