A Note on the Distribution of the Extreme Degrees of a Random Graph via the Stein-Chen Method

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-02 DOI:10.1007/s11009-024-10091-0

Yaakov Malinovsky

引用次数: 0

Abstract

We offer an alternative proof, using the Stein-Chen method, of Bollobás’ theorem concerning the distribution of the extreme degrees of a random graph. Our proof also provides a rate of convergence of the extreme degree to its asymptotic distribution. The same method also applies in a more general setting where the probability of every pair of vertices being connected by edges depends on the number of vertices.

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通过 Stein-Chen 方法研究随机图极值度分布的说明

我们使用斯坦因-陈方法，提供了关于随机图的极值分布的波尔洛巴斯定理的另一种证明。我们的证明还提供了极值度向其渐近分布的收敛率。同样的方法也适用于更一般的情况，即每对顶点被边连接的概率取决于顶点的数量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.