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Compared to the classical binomial random (hyper)graph model, the study ofrandom regular hypergraphs is made more challenging due to correlations betweenthe occurrence of different edges. We develop an edge-switching technique forhypergraphs which allows us to show that these correlations are limited for alarge range of densities. This extends some previous results of Kim, Sudakovand Vu for graphs. From our results we deduce several corollaries on subgraphcounts in random $d$-regular hypergraphs. We also prove a conjecture of Dudek,Frieze, Ruci\'nski and \v{S}ileikis on the threshold for the existence of an$\ell$-overlapping Hamilton cycle in a random $d$-regular $r$-graph.  Moreover, we apply our results to prove bounds on the query complexity oftesting subgraph-freeness. The problem of testing subgraph-freeness in thegeneral graphs model was first studied by Alon, Kaufman, Krivelevich and Ron,who obtained several bounds on the query complexity of testingtriangle-freeness. We extend some of these previous results beyond the trianglesetting and to the hypergraph setting.

Edge correlations in random regular hypergraphs and applications to subgraph testing