Current directions in the combinatorics of free probability

自由概率组合学的当前方向

• 批准号: 203195-2010
• 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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=593784
• 关键词: Current; directions; combinatorics; free; probability

Free probability is 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 free noncommutative random variables. Free probability originated in the 1980s, as a line of attacking some longstanding problems about free products of operator algebras. Since then, it has emerged as a subject in its own right, with connections to several other parts of mathematics, and (via its relation to random matrices) with connections to the study of wireless communications in electrical engineering.

自由概率（英语：Free probability）是一种平行于经典概率的研究，在这种背景下，张量积被自由乘积所取代，独立随机变量被自由非交换随机变量所取代。自由概率起源于20世纪80年代，作为解决算子代数的自由积问题的一条路线。从那时起，它已经成为一个独立的学科，与数学的其他几个部分有联系，并且（通过它与随机矩阵的关系）与电气工程中的无线通信研究有联系。