eBook PDF Download Digital Library
Author: Alexandru Nica
Publisher: Cambridge University Press
Published: 2006-09-07
Total Pages: 430
ISBN-13: 0521858526
DOWNLOAD EBOOK →This 2006 book is a self-contained introduction to free probability theory suitable for an introductory graduate level course.
Author: James A. Mingo
Publisher: Springer
Published: 2017-06-24
Total Pages: 336
ISBN-13: 1493969420
DOWNLOAD EBOOK →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.
Author: Roland Speicher
Publisher: American Mathematical Soc.
Published: 1998
Total Pages: 105
ISBN-13: 0821806939
DOWNLOAD EBOOK →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.
Author: Dimitri Bertsekas
Publisher: Athena Scientific
Published: 2008-07-01
Total Pages: 544
ISBN-13: 188652923X
DOWNLOAD EBOOK →An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems.
Author: Jim Pitman
Publisher: Springer Science & Business Media
Published: 2006-05-11
Total Pages: 257
ISBN-13: 354030990X
DOWNLOAD EBOOK →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.
Author: Dan V. Voiculescu
Publisher: American Mathematical Soc.
Published: 1997
Total Pages: 322
ISBN-13: 0821806750
DOWNLOAD EBOOK →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.
Author: R. C. Bose
Publisher:
Published: 1984-03-19
Total Pages: 264
ISBN-13:
DOWNLOAD EBOOK →A ``hands-on'' constructive and computational approach to combinatorial topics with real-life modern applications. Provides a simple treatment of the subject. Introduces topics such as counting, designs and graphs. The notation is standard and kept to a minimum. Chapters end with historical remarks and suggestions for further reading.
Author: Roman Vershynin
Publisher: Cambridge University Press
Published: 2018-09-27
Total Pages: 299
ISBN-13: 1108415199
DOWNLOAD EBOOK →An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
Author: Béla Bollobás
Publisher: Cambridge University Press
Published: 1986-07-31
Total Pages: 196
ISBN-13: 9780521337038
DOWNLOAD EBOOK →Combinatorics is a book whose main theme is the study of subsets of a finite set. It gives a thorough grounding in the theories of set systems and hypergraphs, while providing an introduction to matroids, designs, combinatorial probability and Ramsey theory for infinite sets. The gems of the theory are emphasized: beautiful results with elegant proofs. The book developed from a course at Louisiana State University and combines a careful presentation with the informal style of those lectures. It should be an ideal text for senior undergraduates and beginning graduates.
Author: Ross G. Pinsky
Publisher: Springer
Published: 2014-08-09
Total Pages: 165
ISBN-13: 3319079654
DOWNLOAD EBOOK →The primary intent of the book is to introduce an array of beautiful problems in a variety of subjects quickly, pithily and completely rigorously to graduate students and advanced undergraduates. The book takes a number of specific problems and solves them, the needed tools developed along the way in the context of the particular problems. It treats a melange of topics from combinatorial probability theory, number theory, random graph theory and combinatorics. The problems in this book involve the asymptotic analysis of a discrete construct, as some natural parameter of the system tends to infinity. Besides bridging discrete mathematics and mathematical analysis, the book makes a modest attempt at bridging disciplines. The problems were selected with an eye toward accessibility to a wide audience, including advanced undergraduate students. The book could be used for a seminar course in which students present the lectures.
