  We study the problem of community detection in a random hypergraph model
which we call the stochastic block model for $k$-uniform hypergraphs ($k$-SBM).
We investigate the exact recovery problem in $k$-SBM and show that a sharp
phase transition occurs around a threshold: below the threshold it is
impossible to recover the communities with non-vanishing probability, yet above
the threshold there is an estimator which recovers the communities almost
asymptotically surely. We also consider a simple, efficient algorithm for the
exact recovery problem which is based on a semidefinite relaxation technique.
