Threshold existence for random NAE-$k$-SAT and random hypergraph $2$-colourability

Abstract

The existence of limiting threshold densities for random hypergraph $2$-colourability and random NAE-$k$-SAT was conjectured in earlier work, including Achlioptas and Moore [RANDOM 2002] and Coja-Oghlan and Panagiotou [STOC 2012]. We prove these conjectures for all $k\ge 3$. We also show that ${\alpha }_k^{2-\mathrm{col}}\le {\alpha }_k^{\mathrm{NAE}}$ for each $k\ge 3$.