Dense multigraphon-valued stochastic processes and edge-changing dynamics in the configuration model

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-04-27 DOI:10.1214/22-aap1889

A. Rollin, Zhuohui Zhang

引用次数: 1

Abstract

Time-evolving random graph models have appeared and have been studied in various fields of research over the past decades. However, the rigorous mathematical treatment of large graphs and their limits at the process-level is still in its infancy. In this article, we adapt the approach of Athreya, den Hollander and R\"ollin (2021+) to the setting of multigraphs and multigraphons, introduced by Kolossv\'ary and R\'ath (2011). We then generalise the work of R\'ath (2012) and R\'ath and Szak\'acs (2012), who analysed edge-flipping dynamics on the configuration model -- in contrast to their work, we establish weak convergence at the process-level, and by allowing removal and addition of edges, these limits are non-deterministic.

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配置模型中的稠密多图值随机过程和边变化动力学

在过去的几十年里，时间演化随机图模型已经出现，并在各个研究领域得到了研究。然而，在过程层面上对大型图及其极限的严格数学处理仍处于初级阶段。本文采用了Athreya的方法，den Hollander和R“ollin（2021+）对Kolossv’ary和R’ath（2011）引入的多重图和多重图的设置进行了讨论。然后，我们对R‘ath（2012）和R‘ath以及Szak’acs（2012）的工作进行了概括，谁分析了配置模型上的边缘翻转动力学——与他们的工作相反，我们在过程级别建立了弱收敛性，通过允许删除和添加边缘，这些限制是不确定的。

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.