Measure concentration and information distances (A04)

测量浓度和信息距离（A04）

• 批准号: 366760977
• 金额: --
• 依托单位: Arbeitsgruppe Probability Theory and Mathematical Statistics
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/366760977?language=en
• 关键词: Measure; concentration; information; distances; A04

In this project we shall investigate concentration of measure and large deviation tail bounds for Lipschitz type functions of high dimensional vectors of observations for various distribution classes. The large deviation behavior of functions on Euclidean spaces and on metric spaces and graphs is studied by means of gradients respectively finite differences. Furthermore, we shall investigate the convergence in the central limit theorem for sums of independent random elements in classical, non commutative and related probability theories in terms of appropriate information distances.

在这个项目中，我们将研究各种分布类别的高维观测向量的Lipschitz型函数的测量浓度和大偏差尾界。利用梯度有限差分分别研究了函数在欧氏空间和度量空间及图上的大偏差行为。此外，我们将研究经典、非交换和相关概率论中独立随机元素和的中心极限定理在适当信息距离下的收敛性。