Concentration of measure, large deviations, normal approximation and applications

测量集中、大偏差、正态近似及应用

• 批准号: 1309618
• 负责人: Sourav Chatterjee
• 金额: $ 36万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-07-01 至 2014-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1309618&HistoricalAwards=false
• 关键词: Concentration; measure; large; deviations; normal

It is proposed to study several problems in probability. One class of problems concerns the phenomenon of localization under the occurrence of a rare event, with applications to problems ranging from nonlinear dispersive equations to random graphs. A second class of problems involves cutting-edge issues in concentration of measure, particularly related to a topic called "superconcentration". The PI is proposing to writing a book-length monograph on these topics, compiling a bunch of results that he proved in previous work together with some new results and ideas. Finally, a third class of problems centers around a continuation of the proposer's earlier work of normal approximation in modern problems.Concentration of measure and large deviations are basic mathematical tools that are frequently used in statistics, computer science, engineering, physics, and many other fields. In this proposal, the PI has outlined a plan that may shed light on some fundamental issues in large deviations and concentration of measure, with applications to open questions in partial differential equations, random graphs and networks, and several other topics. The purpose of the proposed book-length monograph is to elucidate the ideas to a broad audience.

建议研究一些概率问题。一类问题涉及在罕见事件发生下定位的现象，其应用于从非线性色散方程到随机图的问题。第二类问题涉及量度集中的尖端问题，特别是与称为“超浓度”的主题相关的问题。 PI提议编写有关这些主题的书长专着，并汇编了他在以前的工作中证明的一堆结果以及一些新的结果和想法。 最后，第三类问题围绕着提议者在现代问题中的正常近似工作的延续。测量和较大偏差的集中是基本的数学工具，这些工具经常用于统计，计算机科学，工程，物理和许多其他领域。在此提案中，PI概述了一项计划，该计划可能会阐明大偏差和量度集中的某些基本问题，并应用于以部分微分方程，随机图和网络以及其他几个主题开放问题。拟议的书长专着的目的是向广泛的受众阐明这些想法。