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Convergence in homogeneous random graphs

Tomasz Łuczak·Saharon Shelah
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Abstract

For a sequence p=(p(1),p(2), ...) let G(n,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,p), can be affected by the behaviour of p and the strength of the language we use.

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Tomasz Łuczak, Saharon Shelah. 1995-01-15. Convergence in homogeneous random graphs. https://arxiv.org/abs/math/9501221

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