Mathematical Sciences: Evolution of Interacting Particle Systems

数学科学：相互作用粒子系统的演化

• 批准号: 8901545
• 负责人: Maury Bramson
• 金额: $ 10.66万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-05-15 至 1992-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8901545&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Evolution; Interacting; Particle

This research concerns the area of interacting particle systems in probability theory, the theory of random walks in random environments, and the understanding of branching processes. This project should contribute to understanding the general theory of particle systems, the rate of diffusion of random walks in random environments, and the limiting density of branching random walks. Work on particle systems dates to about 1970 and has been motivated by examples of such systems from the biological sciences, statistical mechanics, and cybernetics. Typically, large numbers of particles are assumed to interact according to some rule; one is interested in the limiting behavior of such systems after a long time. Basic systems such as the contact process, voter model, and coalescing and annihilating random walks are simple models for the propagation of a species, the spread of disease, or the state of a chemical reaction.

这项研究涉及相互作用粒子的领域 概率论中的系统， 随机环境，以及对分支的理解 流程. 该项目应有助于了解 粒子系统的一般理论，扩散速率， 随机环境中的随机游动，以及 分支随机游动 关于粒子系统的工作可以追溯到1970年， 受生物学中这种系统的例子的启发， 科学、统计力学和控制论。 典型地， 假设大量粒子根据下式相互作用： 一些规则;人们对这种限制行为感兴趣 系统经过很长时间。 联系人等基本系统 进程、投票者模型、合并和零化随机 散步是一个物种繁殖的简单模型， 疾病的传播或化学反应的状态。