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We prove a conjecture of Linial that every monotone graph property has a sharp threshold. This follows from the following theorem. Let V n ( p ) = { 0 , 1 } n V_n(p)= \\{0,1\\}^n denote the Hamming space endowed with the probability measure μ p \\mu _p defined by μ p ( ϵ 1 , ϵ 2 , … , ϵ n ) = p k ⋅ ( 1 − p ) n − k \\mu _p (\\epsilon _1, \\epsilon _2, \\dots , \\epsilon _n)= p^k \\cdot (1-p)^{n-k} , where k = ϵ 1 + ϵ 2 + ⋯ + ϵ n k=\\epsilon _1 +\\epsilon _2 +\\cdots +\\epsilon _n . Let A A be a monotone subset of V n V_n . 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Every monotone graph property has a sharp threshold 论文

Every monotone graph property has a sharp threshold · 作者