We prove that random hypergraphs are asymptotically almost surely resiliently Hamiltonian. Specifically, for any \(\gamma›0\) and \(k\ge3\), we show that asymptotically almost surely, every subgraph of the binomial random \(k\)-uniform hypergraph \(G^{(k)}\big(n,n^{\gamma-1}\big)\) in which all \((k-1)\)-sets are contained in at least \(\big(\tfrac12+2\gamma\big)pn\) edges has a tight Hamilton cycle. This is a cyclic ordering of the \(n\) vertices such that each consecutive \(k\) vertices forms an edge.

Mathematics Subject Classifications: 05C80, 05C35

Keywords: Random graphs, hypergraphs, tight Hamilton cycles, resilience