On the convergence of probabilities of the random graphs' properties expressed by first-order formulae with a bounded quantifier depth
Combinatorics
2013-04-04 v1
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).
Keywords
Cite
@article{arxiv.1304.0896,
title = {On the convergence of probabilities of the random graphs' properties expressed by first-order formulae with a bounded quantifier depth},
author = {Maksim Zhukovskii},
journal= {arXiv preprint arXiv:1304.0896},
year = {2013}
}