Zero One Laws for Graphs with Edge Probabilities Decaying with Distance, Part Ii Sh517
نویسنده
چکیده
Fixing an irrational α ∈ (0, 1) we prove the 0-1 law for the random graph on [n] with the probability of {i, j} being an edge being essentially 1 |i−j|α .
منابع مشابه
Zero one laws for graphs with edge probabilities decaying with distance
Let Gn be the random graph on [n] = {1, . . . , n} with the possible edge {i, j} having probability being p|i−j| = 1/|i − j| , α ∈ (0, 1) irrational. We prove that the zero one law (for first order logic) holds. We thank John Baldwin and Shmuel Lifsches for helping in various ways and stages to make the paper more user friendly. The research partially supported by the United States – Israel Bin...
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Let Gn be the random graph on [n] = {1, . . . , n} with the possible edge {i, j} having probability p|i−j| = 1/|i− j| for j 6= i, i+ 1, i− 1 with α ∈ (0, 1) irrational. We prove that the zero-one law (for first order logic) holds. 0. Introduction. On 0-1 laws see expository papers, e.g. Spencer [Sp]. In Łuczak–Shelah [LuSh 435] the following probabilistic context was investigated. Let p̄ = 〈pi :...
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