Asymptotic geometric analysis, random matrices and related topics

渐近几何分析、随机矩阵及相关主题

• 批准号: 251088-2011
• 负责人: Litvak, Alexander
• 金额: $ 1.31万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2014
• 资助国家: 加拿大
• 起止时间: 2014-01-01 至 2015-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=547649
• 关键词: Asymptotic; geometric; analysis; random; matrices

The project concentrates on several related directions of Asymptotic Geometric Analysis (AGA). This field is concerned with geometric and linear properties of finite dimensional objects, such as convex sets and normed spaces, especially with the characteristic behavior that emerges when the dimension, or a number of other relevant free parameters, is suitably large or tends to infinity. High-dimensional systems are very frequent in mathematics and applied sciences, hence, understanding high-dimensional phenomena is becoming increasingly important. The last decade has seen a tremendous growth of AGA, with the development of new powerful techniques, mainly of probabilistic nature. By virtue of AGA's general framework, methods, and its impact on related fields, AGA can be situated at the "crossroads" of many branches of mathematics: functional analysis, convex and discrete geometry, and several areas of probability.

该项目集中在渐近几何分析（AGA）的几个相关方向上。该字段与有限维对象的几何和线性特性有关，例如凸组和规范空间，尤其是当尺寸或许多其他相关的自由参数时出现的特征行为非常大，或者是无限的。高维系统在数学和应用科学方面非常频繁，因此，了解高维现象变得越来越重要。在过去的十年中，AGA的增长巨大，随着新的强大技术的发展，主要是概率性质。借助AGA的一般框架，方法及其对相关领域的影响，AGA可以位于数学许多分支的“十字路口”：功能分析，凸和离散几何形状以及几个概率领域。