  Delete the edges of a Kneser graph independently of each other with some
probability: for what probabilities is the independence number of this random
graph equal to the independence number of the Kneser graph itself? We prove a
sharp threshold result for this question in certain regimes. Since an
independent set in the Kneser graph is the same as a uniform intersecting
family, this gives us a random analogue of the Erd\H{o}s-Ko-Rado theorem.
