热力学条件下空间生灭过程局部统计的泛函中心极限定理

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-10-01 DOI:10.1214/22-aap1912

Efe Onaran, Omer Bobrowski, Robert J. Adler

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引用次数: 1

摘要

我们给出了在动态泊松过程上定义的局部泛函在过程水平上的正态逼近结果。我们在这里研究的动力学是马尔可夫生-死过程的动力学。我们在所谓的热力学条件下证明了泛函极限定理。我们的结果适用于随机几何文献中一些感兴趣的函数，包括随机几何图中的子图和分量计数。

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Functional central limit theorems for local statistics of spatial birth–death processes in the thermodynamic regime

We present normal approximation results at the process level for local functionals defined on dynamic Poisson processes in Rd. The dynamics we study here are those of a Markov birth–death process. We prove functional limit theorems in the so-called thermodynamic regime. Our results are applicable to several functionals of interest in the stochastic geometry literature, including subgraph and component counts in the random geometric graphs.

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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.