  We establish that in the large degree limit, the value of certain
optimization problems on sparse random hypergraphs is determined by an
appropriate Gaussian optimization problem. This approach was initiated in Dembo
et. al.(2016) for extremal cuts of graphs. The usefulness of this technique is
further illustrated by deriving the optimal value for Max $q$-cut on
Erd\H{o}s-R\'enyi and random regular graphs, Max XORSAT on Erd\H{o}s-R\'enyi
hypergraphs, and the min-bisection for the Stochastic Block Model.
