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

IF 1 4区数学 Q3 STATISTICS & PROBABILITY

Methodology and Computing in Applied Probability 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

Methodology and Computing in Applied Probability 数学-统计学与概率论

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Methodology and Computing in Applied Probability will publish high quality research and review articles in the areas of applied probability that emphasize methodology and computing. Of special interest are articles in important areas of applications that include detailed case studies. Applied probability is a broad research area that is of interest to many scientists in diverse disciplines including: anthropology, biology, communication theory, economics, epidemiology, finance, linguistics, meteorology, operations research, psychology, quality control, reliability theory, sociology and statistics. The following alphabetical listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interests: -Algorithms- Approximations- Asymptotic Approximations & Expansions- Combinatorial & Geometric Probability- Communication Networks- Extreme Value Theory- Finance- Image Analysis- Inequalities- Information Theory- Mathematical Physics- Molecular Biology- Monte Carlo Methods- Order Statistics- Queuing Theory- Reliability Theory- Stochastic Processes