A new concept of independence in noncommutative probability theory.

非交换概率论中独立性的新概念。

• 批准号: DE150100030
• 负责人: Dr Dmitriy Zanin
• 金额: $ 20.7万
• 依托单位: The University of New South Wales
• 依托单位国家: 澳大利亚
• 项目类别: Discovery Early Career Researcher Award
• 财政年份: 2015
• 资助国家: 澳大利亚
• 起止时间: 2015-06-30 至 2018-06-29
• 项目状态: 已结题
• 来源: https://dataportal.arc.gov.au/RGS/Web/Grants/DE150100030
• 关键词: new; concept; independence; noncommutative; probability

The concept of independence lies at the very core of the probability theory. Many attempts to establish the general notion of independence in noncommutative probability theory have led to only two examples so far: the classical (commutative) independence and the free one introduced by Voiculescu. Every other approach has failed to demonstrate the analogues of the key probabilistic results, such as the Law of Large Numbers and the Central Limit Theorem. There is an urgent need for new efficient methodology. This project aims to develop an approach to the independence in terms of mixed momenta and to find new examples of independence besides the ones mentioned above.

独立性的概念是概率论的核心。许多试图建立一般概念的独立性在非交换概率论导致只有两个例子，迄今为止：经典（交换）独立性和自由的Voiculescu介绍。所有其他方法都未能证明关键概率结果的类似物，例如大数定律和中心极限定理。迫切需要新的有效方法。这个项目的目的是发展一种方法的独立性的混合动量，并找到新的例子，除了上述的独立性。