Free Probability Theory
Free Probability Theory
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自由概率论
DOI：
10.1365/s13291-016-0150-5
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
R. Speicher
中科院分区：
文献类型：
--
作者：
R. Speicher
这篇文章是对自由概率论世界的邀请。这个理论是由Dan Voiculescu在20世纪80年代初提出的，并从那时起发展成为一个充满活力和非常活跃的理论，与许多不同的数学分支联系在一起。我们将激发Voiculescu的基本概念“自由”，并将其与表示论，随机矩阵和算子代数的问题。“非交换分布”的概念是该理论的中心目标之一，有待于更深入的理解。
This article is an invitation to the world of free probability theory. This theory was introduced by Dan Voiculescu at the beginning of the 1980’s and has developed since then into a vibrant and very active theory which connects with many different branches of mathematics. We will motivate Voiculescu’s basic notion of “freeness”, and relate it with problems in representation theory, random matrices, and operator algebras. The notion of “non-commutative distributions” is one of the central objects of the theory and awaits a deeper understanding.