Random permutations and partitions with structural constraints

具有结构约束的随机排列和划分

• 批准号: 2106382
• 金额: --
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2018
• 资助国家: 英国
• 起止时间: 2018 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2106382
• 关键词: Random; permutations; partitions; structural; constraints

The project will focus on the asymptotic study of random combinatorial structures exemplified by partitions and permutations subject to various constraints, e.g. on the type of parts or their multiplicities. This is an active topic of research, with exciting links to certain quantum systems where partitions appear naturally due to quantization of energy. As another example, random permutations with suitable distributions depending on the cycle structure may model particle systems with "selective" interaction. The interest of research will be both on the typical behaviour (such as the "limit shape") and on extreme values (e.g., statistics of small cycles or the asymptotic size of a giant component).

该项目将重点关注随机组合结构的渐近研究，以受各种约束的划分和排列为例，例如关于零件的类型或其多样性。这是一个活跃的研究主题，与某些量子系统有着令人兴奋的联系，在这些系统中，由于能量的量子化而自然出现分区。作为另一个例子，取决于循环结构的具有适当分布的随机排列可以模拟具有“选择性”相互作用的粒子系统。研究的兴趣将集中在典型行为（例如“极限形状”）和极值（例如小周期的统计或巨型组件的渐近大小）上。