Lectures on the Combinatorics of Free Probability: Transforms and models
Lectures on the Combinatorics of Free Probability: Transforms and models
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DOI：
10.1017/cbo9780511735127
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发表时间：
2006
期刊：
影响因子：
--
通讯作者：
A. Nica;R. Speicher
中科院分区：
文献类型：
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作者：
A. Nica;R. Speicher
自由概率论研究一类特殊的“非交换”随机变量，它们出现在希尔伯特空间上的算子和一个大的随机矩阵中。自20世纪80年代出现以来，自由概率已经发展成为一个与其他数学领域有着密切联系的数学领域，如算子代数，经典概率论，随机矩阵，组合学，对称群的表示论。自由概率还与更多的应用科学领域联系在一起，例如电气工程中的无线通信。这本书是第一次给一个独立的和全面的介绍自由概率论有其主要重点的组合方面。卷的设计，使它可以作为一个文本的介绍性课程（在高级本科或开始研究生水平），也非常适合个人研究的自由概率。
Free Probability Theory studies a special class of'noncommutative'random variables, which appear in the context of operators on Hilbert spaces and in one of the large random matrices. Since its emergence in the 1980s, free probability has evolved into an established field of mathematics with strong connections to other mathematical areas, such as operator algebras, classical probability theory, random matrices, combinatorics, representation theory of symmetric groups. Free probability also connects to more applied scientific fields, such as wireless communication in electrical engineering. This book is the first to give a self-contained and comprehensive introduction to free probability theory which has its main focus on the combinatorial aspects. The volume is designed so that it can be used as a text for an introductory course (on an advanced undergraduate or beginning graduate level), and is also well-suited for the individual study of free probability.