Mathematical Sciences: Topics in Probability Theory: Statistical Mechanics Type Models and Sums of Independent Random Variables

数学科学：概率论主题：统计力学类型模型和独立随机变量之和

• 批准号: 9301501
• 负责人: Harry Kesten
• 金额: --
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9301501&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Probability; Theory

Several problems in probability theory are to be studied. The first three concern models which are closely related to statistical physics, while the last one deals with the more traditional topic of sums of independent, identically distributed random variables. Particular problems include finding bounds on the radius of a stochastic growth model, investigating some properties of random resistor networks, and studying the asymptotic shape of first and last passage percolation. This research will investigate some probabilistic models inspired by statistical physics. These include critical phenomena in percolation theory, diffusion limited aggregation , and first-passage percolation. In addition, the investigator will also look at criteria for divergence of sums of independent, identically distributed random variables from which some large summands have been removed.

要研究概率论中的几个问题。 前三个模型与以下方面密切相关： 统计物理学，而最后一个处理更多的 独立同分布和的传统话题 随机变量 特别的问题包括找到 随机增长模型的半径，研究一些 随机电阻网络的性质，并研究了 第一次和最后一次通过渗流的渐近形状。 本研究将探讨一些机率模型 受到统计物理学的启发 其中包括关键的 渗透理论中的现象，扩散限制聚集， 和第一通道渗滤。 此外，调查员 还将研究独立， 同分布的随机变量， 已删除summands。