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

On the stability of the Erd\H{o}s-Ko-Rado theorem