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.

本项目主要集中在大量的概率模型上，这些模型涉及到聚结和碎裂现象。我们提出了一种统一的方法来研究在各种背景下分别引起显著关注的一大类模型。一个特别的目标是给出新的和强有力的标度极限描述，并理解相变和自组织临界现象。这些主题在物理学、概率论、离散数学和复杂系统的广泛领域中具有重要意义。所研究的一些系统还将作为分析某些空间模型的工具，这些空间模型由于与量子自旋系统和超流等物理主题的关系而引起了人们的兴趣。该项目的最后一部分集中在随机交织上，一种新兴的渗透和侵蚀模型，其中长程相互作用起着重要作用。我们将联合收割机的概率，几何和分析工具来描述离散随机结构的出现，并了解他们的属性如何不同于传统的渗流模型。

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

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

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

The Brownian continuum random tree as the unique solution to a fixed point equation

布朗连续随机树作为定点方程的唯一解

• DOI: 10.1214/ecp.v20-4250
• 发表时间: 2015
• 期刊: Electronic Communications in Probability
• 影响因子: 0.5
• 作者: Albenque M