The threshold for fractional clique decompositions of random hypergraphs, via matrix scaling

Let $δ^*_{k,r}$ be the fractional $K_r^{(k)}$-decomposition threshold in minimum codegree. For fixed $k\ge2$, $r\ge k+1$ and $\varepsilon>0$, we prove that every $n$-vertex $k$-uniform hypergraph $G$ with minimum codegree at least $(δ^*_{k,r}+\varepsilon)n$ admits, with high probability, a fractiona