Let F be a strictly k-balanced k-uniform hypergraph with e(F)≥∣F∣−k+1 and maximum co-degree at least two. The random greedy F-free process
constructs a maximal F-free hypergraph as follows. Consider a random ordering
of the hyperedges of the complete k-uniform hypergraph Knk on n
vertices. Start with the empty hypergraph on n vertices. Successively
consider the hyperedges e of Knk in the given ordering, and add e to
the existing hypergraph provided that e does not create a copy of F. We
show that asymptotically almost surely this process terminates at a hypergraph
with O~(nk−(∣F∣−k)/(e(F)−1)) hyperedges. This is best possible up
to logarithmic factors