Noncommutative Probability Aspects of Operator Algebra Theory

算子代数理论的非交换概率方面

• 批准号: 0079945
• 负责人: Dan-Virgil Voiculescu
• 金额: --
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-06-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0079945&HistoricalAwards=false
• 关键词: Noncommutative; Probability; Aspects; Operator; Algebra

AbstractVoiculescuDan Voiculescu will study operator algebras in connection with free probability. He will emphasize applications of free entropy to operator algebras as well as the problems in operator algebras and random matrix theory posed by the development and unification of approaches to free entropy. There are also connections to masterfields in certain models in physics. Dan Voiculescu also intends to study noncommutative generalizations of the difference - quotient and of the Hilbert transform, in connection with duality for a certain class of coalgebras arising in free probability. Free probability theory is a highly noncommutative parallel to basic probability theory , modelling the asymptotic behavior of large random matrices as their size increases. One main focus will be on free entropy, the quantity which plays in this context the role of Shannon's information-theoretic entropy. Applications are in mathematics to von Neumann algebras and to random matrices, as well as to some models in physics .

Voiculescu丹Voiculescu将研究算子代数与自由概率。他将强调应用自由熵算子代数以及问题的算子代数和随机矩阵理论所造成的发展和统一的办法，以自由熵。物理学中的某些模型也与大师领域有联系。丹Voiculescu还打算研究noncommutative一般化的差商和希尔伯特变换，在连接与对偶的某一类coalgebras所产生的自由概率。自由概率论是一个高度非交换的平行于基本概率论，建模的渐近行为的大型随机矩阵的大小增加。一个主要的焦点将是自由熵，在这方面发挥作用的香农的信息论熵的数量。 应用在数学冯诺依曼代数和随机矩阵，以及一些模型在物理学。