Random fragmentation-coalescence processes out of equilibrium

随机分裂-聚结过程失去平衡

• 批准号: EP/S036202/2
• 负责人: Andreas Kyprianou
• 金额: $ 10.66万
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FS036202%2F2
• 关键词: Random; fragmentation; coalescence; processes; out

Stochastic coalescence models describe how blocks of mass randomly join together over time according certain rules of random evolution. Conversely, stochastic fragmentation models describe how blocks of mass break apart over time, again according to certain rules of random evolution. Processes with one or antoher of theses actions, have been widely investigated. Coalescence has been an active field since the seminal work of Smoluchowski 100 years ago. Fragmentation is a more recently investigated phenomenon, with the the main foundational development starting from the work of Bertoin in the early 2000s. Little has been done, howver, in the rigorous mathematical literature regarding the combination of both actions of fragmentation and coalescence. Despite this fact, there is a strong motivation for the treatement of such models in the scientific literature thanks to applications in physical chemistry and genealogy, and more recently in group dynamics in the social sciences and biology.The purpose of this project is to thus investigate new probabilistic techniques to characterise the dynamics of tractable families of stochastic fragmentation-coalescence processes. One of the mathematical difficulties with such models is that they do not possess so-called reversibility properties. This means that when considering such processes time reversed, they do not exibit the mathematical convenience that would allow known analytical techniques to be used. For this reason, their analysis is generally difficult.In this proposal we will look at some special classes of fragmentation-coalescence models that were only very recently introduced into the literature (by the PI and CI as well as others) and for which some degree of tractability has already been demonstrated. We will use a mixture of techniques to analyse their stationary and quasi-stationary behaviour, exposing currently unknown behaviours and laying out a deeper understanding of how such models can be treated in general.

随机聚结模型描述了块体如何根据一定的随机演化规则随时间随机地结合在一起。相反，随机碎裂模型描述了质量块如何随着时间的推移而碎裂，同样是根据随机演化的某些规则。具有上述一种或多种作用的过程已被广泛研究。自100年前Smoluchowski的开创性工作以来，聚结一直是一个活跃的领域。碎片化是一个最近研究的现象，主要的基础发展始于21世纪初Bertoin的工作。然而，在严谨的数学文献中，关于碎裂和聚结这两种作用的结合，几乎没有做过什么。尽管这一事实，有一个强烈的动机，在科学文献中的应用，由于在物理化学和系谱学，以及最近在社会科学和biology.The目的的群体动力学的这种模型的解释，因此，本项目的目的是调查新的概率技术，以解释的随机破碎-合并过程的易处理的家庭的动态。这种模型的数学困难之一是它们不具有所谓的可逆性。这意味着，当考虑这样的过程时间反转，他们不显示数学上的方便，将允许使用已知的分析技术。因此，对它们的分析通常是困难的。在这个建议中，我们将研究一些特殊的碎裂-聚结模型，它们是最近才被引入文献中的（由PI和CI以及其他人），并且已经证明了它们的某种程度的易处理性。我们将使用各种技术来分析它们的静态和准静态行为，揭示目前未知的行为，并深入了解如何处理这些模型。

项目成果

Ancestral reproductive bias in branching processes

分支过程中的祖先生殖偏差

• DOI: 10.1007/s00285-023-01907-7
• 发表时间: 2023
• 期刊: Journal of Mathematical Biology
• 影响因子: 1.9
• 作者: Cheek D

Multitype ?-coalescents

多型β-成膜助剂

• DOI: 10.1214/22-aap1891
• 发表时间: 2023
• 期刊: The Annals of Applied Probability
• 作者: Johnston S