The Linear $q$-Hypergraph Process

We analyze a random greedy process to construct $q$-uniform linear hypergraphs using the differential equation method. We show for $q=o(\sqrt{\log n})$, that this process yields a hypergraph with $\frac{n(n-1)}{q(q-1)}(1-o(1))$ edges. We also give some bounds for maximal linear hypergraphs.