Processes of coalescence and fragmentation: phase transitions, scaling limits and self-organised criticality

聚结和分裂过程：相变、尺度限制和自组织临界性

• 批准号: EP/J019496/1
• 负责人: Christina Goldschmidt
• 金额: $ 39.47万
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2013
• 资助国家: 英国
• 起止时间: 2013 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FJ019496%2F1
• 关键词: Processes; coalescence; fragmentation; phase; transitions

This project is focused on a rich collection of probabilistic modelswhich involve phenomena of coalescence and fragmentation.We propose a unified approach to the study of a large class of modelswhich have separately attracted significant attention in a variety ofcontexts.A particular goal is to give new and powerful descriptions of scalinglimits, and to understand phenomena of phase transition andself-organised criticality. Such themes are of considerablesignificance across a wide range of fields in physics, probabilitytheory, discrete mathematics and complex systems.Some of the systems studied will also serve as tools in the analysisof certain spatial models, which are of lively current interest due totheir relationship to quantum spin systems and physical topics such assuperfluidity.The last part of the project centres on random interlacements, anemerging model of percolation and erosion in which long-rangeinteractions play a significant role. We will combine a range ofprobabilistic, geometric and analytic tools to describe the discreterandom structures that emerge, and to understand how their propertiesdiffer from those of traditional percolation models.

该项目的重点集中在丰富的概率模型中，涉及结合和分散现象。我们提出了一种统一的方法来研究大量的模型Swhich，在各种特殊目标中都引起了大量的关注。特定的目标是使Scainginglimits的新颖和强大的刻画描述，以了解缩小的新描述，并了解相位和自学的现象和自我实现的现象。这些主题在物理，概率理论，离散的数学和复杂系统的广泛领域都具有重要意义远程界面发挥了重要作用。我们将结合一系列概况，几何和分析工具，以描述出现的自由和结构，并了解它们与传统渗滤模型的属性如何分化。

项目成果

Chromatic thresholds in dense random graphs

密集随机图中的色阈值

• DOI: 10.1002/rsa.20708
• 发表时间: 2017
• 期刊: Random Structures & Algorithms
• 影响因子: 1
• 作者: Allen P

Quenched Voronoi percolation

淬火 Voronoi 渗透

• DOI: 10.1016/j.aim.2015.09.005
• 发表时间: 2016
• 期刊: Advances in Mathematics
• 影响因子: 1.7
• 作者: Ahlberg D

Inverting the cut-tree transform

反转割树变换

• DOI: 10.1214/18-aihp921
• 发表时间: 2019
• 期刊: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
• 作者: Addario-Berry L

Competition in growth and urns

生长和骨灰盒的竞争

• DOI: 10.1002/rsa.20779
• 发表时间: 2018
• 期刊: Random Structures & Algorithms
• 影响因子: 1
• 作者: Ahlberg D

Critical random graphs and the differential equations technique

临界随机图和微分方程技术

• DOI: 10.1007/s13226-017-0249-0
• 发表时间: 2018
• 期刊: Indian Journal of Pure and Applied Mathematics
• 影响因子: 0.7
• 作者: Bhamidi S