On the Convergence of Probabilities of First-Order Sentences for Recursive Random Graph Models

被引：0

作者：

Zhukovskii, M. E. ^{[1
,2
,3
]}

Malyshkin, Yu A. ^{[1
,4
]}

机构：

[1] Natl Res Univ, Moscow Inst Phys & Technol, Dolgoprudnyi 141701, Moscow Oblast, Russia

[2] Adyghe State Univ, Caucasus Math Ctr, Maykop 385000, Republic Of Ady, Russia

[3] Russian Presidential Acad, Natl Econ & Publ Adm, Moscow 119571, Russia

[4] Tver State Univ, Tver 170100, Russia

来源：

DOKLADY MATHEMATICS | 2020年 / 102卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

recursive random graphs; preferential attachment; first-order logic; zero-one laws;

D O I：

10.1134/S1064562420050464

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study first-order zero-one law and the first-order convergence law for two recursive random graph models, namely, the uniform and preferential attachment models. In the uniform attachment model, a new vertex with edges chosen uniformly is added at every moment, while, in the preferential attachment model, the distribution of second ends of these edges is not uniform, but rather the probabilities are proportional to the degrees of the respective vertices.

引用

页码：384 / 386

页数：3

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