paper

On the convergence of probabilities of the random graphs' properties expressed by first-order formulae with a bounded quantifier depth

arXiv:1304.0896

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).

Cited by in corpus (1)

On the convergence of probabilities of the random graphs' properties expressed by first-order formulae with a bounded quantifier depth · wovepaper