Resilience for tight Hamiltonicity

We prove that random hypergraphs are asymptotically almost surely resiliently Hamiltonian. Specifically, for any γ > 0 and k ≥ 3, we show that asymptotically almost surely, every subgraph of the binomial random k-uniform hypergraph G (k)(n, n γ−1) in which all (k − 1)-sets are contained in at least (1/2 + 2γ) pn edges has a tight Hamilton cycle. This is a cyclic ordering of the n vertices such that each consecutive k vertices forms an edge.