Probability measures on topological groups and related problems in harmonic and functional analysis

拓扑群的概率测度及调和与泛函分析中的相关问题

• 批准号: 238895-2006
• 负责人: Jaworski, Wojciech
• 金额: $ 0.87万
• 依托单位: Carleton University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=363976
• 关键词: Probability; measures; topological; groups; related

Probability Measures on Topological Groups and Related Problems in Harmonic and Functional Analysis The main topic of this research concerns certain aspects of the asymptotic (i.e., large time) behaviour of random walks on groups. Although the theory of random walks has, generally speaking, a strongly applied flavour, this research has to do mainly with the foundations of the theory and its connections to other fields of mathematics. The theory of probability measures and random walks on groups interacts in a nontrivial and deep way with several fields of mathematics. In addition to purely probabilistic methods, mathematical tools of harmonic and functional analysis, ergodic theory, and the theory of topological groups have to be involved to make progress. This interaction very often leads to nontrivial problems and solutions which can be of considerable interest not only within but also outside the theory of probability.

拓扑群上的概率测度及调和与泛函分析中的相关问题本研究的主要课题涉及渐近（即，大时间）行为的随机游动的群体。虽然理论的随机游动，一般来说，一个强烈的应用味道，这项研究主要是做的基础理论和它的连接到其他领域的数学。群上的概率测度和随机游动理论以一种非平凡的和深入的方式与几个数学领域相互作用。除了纯粹的概率方法，数学工具的谐波和功能分析，遍历理论，理论的拓扑群必须参与取得进展。这种相互作用经常导致非平凡的问题和解决方案，这些问题和解决方案不仅在概率论内部而且在概率论之外都具有相当大的意义。