β聚结剂的大尺度行为和流体动力学极限

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-02-01 DOI:10.1214/22-aap1782

Luke Miller, Helmut H. Pitters

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引用次数: 0

摘要

我们用参数a，b>0量化了β聚结剂π={π（t），t≥0}在大尺度上的行为。具体来说，我们研究了π（t）的重标块大小谱及其对{1，…，n}的限制。我们的主要结果是一个大数定律类型的结果，如果π从无穷大降下来。在Kingman聚结的情况下，自Smoluchowski[30]的工作以来，已经知道了这个所谓的流体动力学极限的推导。我们将Smoluchowski的结果推广到β聚结物，并证明如果π从无穷大下降，两个重标光谱

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Large-scale behaviour and hydrodynamic limit of beta coalescents

We quantify the behaviour at large scales of the beta coalescent Π = {Π(t), t ≥ 0} with parameters a, b > 0. Specifically, we study the rescaled block size spectrum of Π(t) and of its restriction Πn(t) to {1, . . . , n}. Our main result is a Law of Large Numbers type of result if Π comes down from infinity. In the case of Kingman’s coalescent the derivation of this so-called hydrodynamic limit has been known since the work of Smoluchowski [30]. We extend Smoluchowski’s result to beta coalescents and show that if Π comes down from infinity both rescaled spectra

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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.