Brownian Motion and Random Partitions

布朗运动和随机分区

• 批准号: 9703691
• 负责人: James Pitman
• 金额: $ 25.2万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9703691&HistoricalAwards=false
• 关键词: Brownian; Motion; Random; Partitions

9703691 Pitman Recent work of the principal investigator and co-authors has made connections between random partitions, random discrete distributions, random trees, and the lengths of excursions of Brownian motion and other stochastic processes. The present project continues the study of these relations and their applications. Sheth's model for gravitational clustering of galaxies leads to problems related to the additive coalescent in which each pair of sets in a partition of a finite set is merging at a rate which is the sum of the sizes of the two sets. Asymptotics of this additive coalescent define a discrete measure valued process which can be constructed by cutting Aldous's continuum random tree at points of a suitable Poisson process. It is proposed to study this and other measure-valued Markov processes which model coalescent phenomena, and to look for novel applications of these processes. Brownian motion provides the doundation of the modern theory of continuous time random processes with continuous paths, and has applications in fields as diverse as physics and mathematical finance. Random partitions find applications to combinatorics, physics and genetics. Statistical models for physical processes of coalescence and fragmentation are of interest in a number of fields. The evolution of a partition of particles into clumps can be variously interpreted, for example, as a partition of atoms into molecules, a partition of molecules into polymers, or a partition of stars into galaxies. In a chemical setting, atoms coalesce to form molecules, and molecules coalesce to form polymers. In a cosmological setting, stars coalesce to form galaxies. The proposed research focuses on models for an irreversible process of coalescence of a partition of a continuum with finite total mass into a finite or countable collection of sub-masses, with conservation of mass.

9703691皮特曼 首席研究员和合著者最近的工作将 在随机划分、随机离散分布、随机树和 布朗运动和其他随机过程的行程。本项目 继续研究这些关系及其应用。Sheth模型 星系的引力聚集导致了与星系中的附加聚结有关的问题。 其中有限集合的划分中的每一对集合以如下速率合并： 这两组的大小。这种加性聚结的渐近性定义了一个离散测度 值过程，它可以通过切割Aldous的连续随机树来构造。 一个合适的Poisson过程。建议研究这个和其他测度值 马尔可夫过程的模型结合现象，并寻找新的应用 这些过程。 布朗运动是现代连续时间理论的基础 随机过程与连续路径，并在不同领域的应用， 物理学和金融数学。随机划分可以应用于组合数学， 物理学和遗传学。聚结物理过程的统计模型 碎片化问题在许多领域引起人们的兴趣。粒子划分的演化 成团可以有不同的解释，例如，作为一个分区的原子成 分子，分子划分成聚合物，或者恒星划分成星系。中 在化学环境中，原子聚结形成分子，分子聚结形成 聚合物在宇宙学背景下，恒星合并形成星系。拟议 研究的重点是模型的一个分区的聚结的不可逆过程， 具有有限总质量的连续统，分成有限或可数的子质量集合， 质量守恒