Free probability: combinatorial and analytic aspects, and interactions with other notions of independence

自由概率：组合和分析方面，以及与其他独立概念的相互作用

• 批准号: RGPIN-2017-04181
• 负责人: Nica, Alexandru
• 金额: $ 1.46万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635205
• 关键词: Free; probability; combinatorial; analytic; aspects

The proposal is in the area of free probability theory - a line of research which parallels aspects of classical probability, in a context where tensor products are replaced by free products, and independent random variables are replaced by freely independent noncommutative random variables. Free probability originated in the 1980s, in connection to problems about free products of operator algebras. Since then, it has emerged as a subject in its own right, with connections to other parts of mathematics such as classical probability, algebraic combinatorics, and the theory of random matrices. Through its connection to random matrices, free probability has found applications in quantum information theory and in the area of wireless communications in electrical engineering.

这个提议是在自由概率论领域——在一个张量积被自由积取代，独立随机变量被自由独立的非交换随机变量取代的背景下，一条与经典概率方面相似的研究路线。自由概率起源于20世纪80年代，与算子代数的自由积问题有关。从那时起，它就成为了一门独立的学科，与数学的其他部分有联系，如经典概率论、代数组合学和随机矩阵理论。通过与随机矩阵的联系，自由概率在量子信息理论和电子工程中的无线通信领域中得到了应用。