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2018
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Proceedings of the American Mathematical Society
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In their seminal work which initiated random graph theory Erdös and Rényi discovered that many graph properties have sharp thresholds as the number of vertices tends to infinity. We prove a conjecture of Linial that every monotone graph property has a sharp threshold. This follows from the following theorem. Let Vn(p) = {0, 1} n denote the Hamming space endowed with the probability measure µp defined by µp( 1 , 2 , . . . , n) = p k · (1 − p) n−k , where k = 1 + 2 + · · · + n. Let A be a

doi:10.1090/s0002-9939-96-03732-x
fatcat:qermec32eregxexboarvkbkele