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 \(G⁽ᵏ⁾(n,nγ-1)\) in which all \((k-1)\)-sets are contained in at least \((12+2γ)pn\) edges has a tight Hamilton cycle. This is a cyclic ordering of the \(n\) vertices such that each consecutive \(k\) vertices forms an edge.