Lectures on the combinatorics of free probability. (English) Zbl 1133.60003

London Mathematical Society Lecture Note Series 335. Cambridge: Cambridge University Press (ISBN 0-521-85852-6/pbk). xv, 417 p. (2006).
Publisher’s description: Free probability theory studies a special class of ‘noncommutative’ random variables, which appear in the context of operators on Hilbert spaces and in the one of 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. The book presents the state of the art of the combinatorial facet of free probability. It gives a friendly and self-contained introduction to the general field of free probability and is written in a style which makes it ideal for use in the presentation of a graduate level course.


60-02 Research exposition (monographs, survey articles) pertaining to probability theory
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