On the number of solutions in random hypergraph 2-colouring

TL;DR

This paper analyzes the distribution of solutions in random hypergraph 2-coloring, establishing a connection between the uniform and planted models, which simplifies understanding solution counts in certain regimes.

Contribution

It determines the limiting distribution of the number of solutions in random hypergraph 2-coloring and shows contiguity with the planted model across all k ≥ 3.

Findings

Distribution of solutions is characterized in a specific density regime.

Random coloring model is contiguous with the planted model.

Results apply to all k ≥ 3.

Abstract

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.