Convergence in homogeneous random graphs

by Luczak and Shelah. [LuSh:435]
Random Structures \& Algorithms, 1995
For a sequence bar {p}=(p(1),p(2), ...) let G(n, bar {p}) denote the random graph with vertex set {1,2, ...,n} in which two vertices i, j are adjacent with probability p(|i-j|), independently for each pair. We study how the convergence of probabilities of first order properties of G(n, bar {p}), can be affected by the behaviour of bar {p} and the strength of the language we use.

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