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: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=453183
• 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.

自由概率是与经典概率的各个方面平行的研究方向，在张量乘积被自由乘积取代，独立随机变量被自由非交换随机变量取代的背景下。 自由概率起源于 20 世纪 80 年代，作为解决算子代数自由乘积一些长期存在的问题的路线。 从那时起，它就成为一门独立的学科，与数学的其他几个部分有联系，并且（通过其与随机矩阵的关系）与电气工程中的无线通信研究有联系。