Lectures on the Combinatorics of Free Probability

Lectures on the Combinatorics of Free Probability
Title Lectures on the Combinatorics of Free Probability PDF eBook
Author Alexandru Nica
Publisher Cambridge University Press
Pages 430
Release 2006-09-07
Genre Mathematics
ISBN 0521858526

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This 2006 book is a self-contained introduction to free probability theory suitable for an introductory graduate level course.

Free Probability and Random Matrices

Free Probability and Random Matrices
Title Free Probability and Random Matrices PDF eBook
Author James A. Mingo
Publisher Springer
Pages 343
Release 2017-06-24
Genre Mathematics
ISBN 1493969420

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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.

Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory

Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory
Title Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory PDF eBook
Author Roland Speicher
Publisher American Mathematical Soc.
Pages 105
Release 1998
Genre Mathematics
ISBN 0821806939

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Free probability theory, introduced by Voiculescu, has developed very actively in the last few years and has had an increasing impact on quite different fields in mathematics and physics. Whereas the subject arose out of the field of von Neumann algebras, presented here is a quite different view of Voiculescu's amalgamated free product. This combinatorial description not only allows re-proving of most of Voiculescu's results in a concise and elegant way, but also opens the way for many new results. Unlike other approaches, this book emphasizes the combinatorial structure of the concept of ``freeness''. This gives an elegant and easily accessible description of freeness and leads to new results in unexpected directions. Specifically, a mathematical framework for otherwise quite ad hoc approximations in physics emerges.

Probability

Probability
Title Probability PDF eBook
Author Rick Durrett
Publisher Cambridge University Press
Pages
Release 2010-08-30
Genre Mathematics
ISBN 113949113X

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This classic introduction to probability theory for beginning graduate students covers laws of large numbers, central limit theorems, random walks, martingales, Markov chains, ergodic theorems, and Brownian motion. It is a comprehensive treatment concentrating on the results that are the most useful for applications. Its philosophy is that the best way to learn probability is to see it in action, so there are 200 examples and 450 problems. The fourth edition begins with a short chapter on measure theory to orient readers new to the subject.

Combinatorial Stochastic Processes

Combinatorial Stochastic Processes
Title Combinatorial Stochastic Processes PDF eBook
Author Jim Pitman
Publisher Springer Science & Business Media
Pages 257
Release 2006-05-11
Genre Mathematics
ISBN 354030990X

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The purpose of this text is to bring graduate students specializing in probability theory to current research topics at the interface of combinatorics and stochastic processes. There is particular focus on the theory of random combinatorial structures such as partitions, permutations, trees, forests, and mappings, and connections between the asymptotic theory of enumeration of such structures and the theory of stochastic processes like Brownian motion and Poisson processes.

Free Probability Theory

Free Probability Theory
Title Free Probability Theory PDF eBook
Author Dan V. Voiculescu
Publisher American Mathematical Soc.
Pages 322
Release 1997
Genre Mathematics
ISBN 0821806750

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This is a volume of papers from a workshop on Random Matrices and Operator Algebra Free Products, held at The Fields Institute for Research in the Mathematical Sciences in March 1995. Over the last few years, there has been much progress on the operator algebra and noncommutative probability sides of the subject. New links with the physics of masterfields and the combinatorics of noncrossing partitions have emerged. Moreover there is a growing free entropy theory.

High-Dimensional Probability

High-Dimensional Probability
Title High-Dimensional Probability PDF eBook
Author Roman Vershynin
Publisher Cambridge University Press
Pages 299
Release 2018-09-27
Genre Business & Economics
ISBN 1108415199

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An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.