On the convergence of probabilities of the random graphs' properties expressed by first-order formulae with a bounded quantifier depth
Abstract
An asymptotic behavior of the probabilities of first-order properties of Erdos-Renyi random graph G(N,p), lnp=-alnN, is studied in the article. We prove the covergence law for formulae with quantifier depth bounded by k when a=1/(k-2).
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