Free Probability and Random Matrices, Softcover reprint of the original 1st ed. 2017 Fields Institute Monographs Series, Vol. 35

This volume opens the world of free probability to a wide variety of readers. From its roots in the theory of operator algebras, free probability has intertwined with non-crossing partitions, random matrices, applications in wireless communications, representation theory of large groups, quantum groups, the invariant subspace problem, large deviations, subfactors, and beyond. This book puts a special emphasis on the relation of free probability to random matrices, but also touches upon the operator algebraic, combinatorial, and analytic aspects of the theory.

The book serves as a combination textbook/research monograph, with self-contained chapters, exercises scattered throughout the text, and coverage of important ongoing progress of the theory. It will appeal to graduate students and all mathematicians interested in random matrices and free probability from the point of view of operator algebras, combinatorics, analytic functions, or applications in engineering and statistical physics.

Covers a variety of different facets of free probability, giving a flavor of the breadth of the subject

Features exercises scattered throughout the text

Showcases basic ideas and results in order to focus on their relation

Includes supplementary material: sn.pub/extras