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.

随机结合模型描述了质量块如何根据某些随机进化的规则随着时间的推移而随机结合在一起。相反，随机碎片模型描述了质量块如何随着时间的推移而分解，这再次根据某些随机进化规则。已广泛研究了具有某个或Antoher的过程。自100年前Smoluchowski开创性工作以来，合并一直是一个活跃的领域。碎片化是最近研究的现象，主要的基础发展始于2000年代初期贝托因的工作。关于碎片化和结合作用的结合，在严格的数学文献中，几乎没有完成。尽管这一事实，由于在物理化学和家谱中的应用以及在社会科学和生物学中的群体动态中的应用，在科学文献中对这种模型进行治疗的动机具有很大的动力。因此，该项目的目的是研究新的概率技术，以表征易于特征的现有片段片段的动力学。这种模型的数学困难之一是它们没有所谓的可逆性。这意味着，当考虑此类过程逆转时，它们不会超越数学便利，从而可以使用已知的分析技术。因此，他们的分析通常很困难。在此提案中，我们将研究一些特殊类别的片段化钙化模型，这些模型最近才被最近引入文献（由PI和CI以及其他文献）引入，并且已经证明了某种程度的拖拉性。我们将使用各种技术来分析其固定和准平台行为，揭露当前未知的行为，并对一般如何处理这种模型进行更深入的了解。

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