Co-degrees resilience for perfect matchings in random hypergraphs

In this paper we prove an optimal co-degrees resilience property for the binomial \(k\)-uniform hypergraph model \(H_{n,p}^k\) with respect to perfect matchings. That is, for a sufficiently large \(n\) which is divisible by \(k\), and \(p\geq C_k\log_n/n\), we prove that with high probability every subgraph \(H\subseteq H^k_{n,p}\) with minimum co-degree (meaning, the number of supersets every set of size \(k-1\) is contained in) at least \((1/2+o(1))np\) contains a perfect matching.