DescriptionOn Erdős-Ko-Rado for Random Hypergraphs o by Arran Hamm Dissertation Director: Jeff Kahn Denote by Hk (n, p) the random k-graph in which each k-subset of {1, . . . , n} is present with probability p, independent of other choices. This dissertation addresses the question: for which p0 will Hk (n, p) satisfy the “Erd˝s-Ko-Rado property” provided that o p > p0 ? This question was first studied by Balogh, Bohman, and Mubayi where they dealt mainly with k < n 2 −γ (for some γ > 0). Our first main result gives the desired p0 when k < cn log(n) (for c < 1 ) and indeed contains the main results of Balogh et 4 1 al. concerning when Hk (n, p) satisfies EKR a.s. (that is, with probability tending to 1 as n → ∞). Additionally, more or less answering a question of Balogh et al., we show: there is a fixed ε > 0 such that if n = 2k + 1 and p > 1 − ε, then Hk (n, p) has the EKR property a.s. ii