Large-scale behaviour and hydrodynamic limit of beta coalescents

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

引用次数: 0

Abstract

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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β聚结剂的大尺度行为和流体动力学极限

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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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

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