  Let r be a fixed constant and let H be an r-uniform, D-regular hypergraph on
N vertices. Assume further that D > N^\epsilon for some \epsilon>0. Consider
the random greedy algorithm for forming an independent set in H. An independent
set is chosen at random by iteratively choosing vertices at random to be in the
independent set. At each step we choose a vertex uniformly at random from the
collection of vertices that could be added to the independent set (i.e. the
collection of vertices v with the property that v is not in the current
independent set I and I \cup {v} contains no edge of H). Note that this process
terminates at a maximal subset of vertices with the property that this set
contains no edge of H; that is, the process terminates at a maximal independent
set. We prove that if H satisfies certain degree and codegree conditions then
there are \Omega(N ((log N) / D)^{1/(r-1)}) vertices in the independent set
produced by the random greedy algorithm with high probability. This result
generalizes a lower bound on the number of steps in the H-free process due to
Bohman and Keevash and produces objects of interest in additive combinatorics.
