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The Kneser hypergraph ${\rm KG}^r_{n,k}$ is an $r$-uniform hypergraph withvertex set consisting of all $k$-subsets of $\{1,\ldots,n\}$ and any collectionof $r$ vertices forms an edge if their corresponding $k$-sets are pairwisedisjoint. The random Kneser hypergraph ${\rm KG}^r_{n,k}(p)$ is a spanningsubhypergraph of ${\rm KG}^r_{n,k}$ in which each edge of ${\rm KG}^r_{n,k}$ isretained independently of each other with probability $p$. The independencenumber of random subgraphs of ${\rm KG}^2_{n,k}$ was recently addressed in aseries of works by Bollob{\'a}s, Narayanan, and Raigorodskii (2016), Balogh,Bollob{\'a}s, and Narayanan (2015), Das and Tran (2016), and Devlin and Kahn(2016). It was proved that the random counterpart of the Erd\H{o}s-Ko-Radotheorem continues to be valid even for very small values of $p$. In this paper,generalizing this result, we will investigate the independence number of randomKneser hypergraphs ${\rm KG}^r_{n,k}(p)$. Broadly speaking, when $k$ is muchsmaller that $n$, we will prove that the random analogue of the Erd\H{o}smatching conjecture is true even for extremely small values of $p$.

On the random version of the Erd\H{o}s matching conjecture