Isomorphisms between random d-hypergraphs

We characterize the size of the largest common induced subgraph of two independent random uniform d-hypergraphs of different sizes with d≥ 3. More precisely, its distribution is asymptotically concentrated on two points, and we obtain as a consequence a phase transition for the inclusion of the smallest hypergraph in the largest one. This generalizes to uniform random d-hypergraphs the results of Chatterjee and Diaconis for uniform random graphs. Our proofs rely on the first and second moment methods.