Combinatorial Theory Of The Free Product With Amalgamation And Operator Valued Free Probability Theory

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

Author : Roland Speicher
Publisher : American Mathematical Soc.
ISBN 13 : 0821806939
Total Pages : 105 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory by : Roland Speicher

Download or read book Combinatorial Theory of the Free Product with Amalgamation and Operator-Valued Free Probability Theory written by Roland Speicher and published by American Mathematical Soc.. This book was released on 1998 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Combinatorial Theory of the Free Product with Amalgamation and

Author : Roland Speicher
Publisher : Oxford University Press, USA
ISBN 13 : 9781470402167
Total Pages : 105 pages
Book Rating : 4.4/5 (21 download)

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Book Synopsis Combinatorial Theory of the Free Product with Amalgamation and by : Roland Speicher

Download or read book Combinatorial Theory of the Free Product with Amalgamation and written by Roland Speicher and published by Oxford University Press, USA. This book was released on 2014-09-11 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: Free probability theory, introduced by Voiculescu, has developed very actively 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 allows re-proving of most of Voiculescu's results and also opens the way for many new results.

Free Probability and Random Matrices

Author : James A. Mingo
Publisher : Springer
ISBN 13 : 1493969420
Total Pages : 336 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Free Probability and Random Matrices by : James A. Mingo

Download or read book Free Probability and Random Matrices written by James A. Mingo and published by Springer. This book was released on 2017-06-24 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lectures on the Combinatorics of Free Probability

Author : Alexandru Nica
Publisher : Cambridge University Press
ISBN 13 : 0521858526
Total Pages : 430 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Lectures on the Combinatorics of Free Probability by : Alexandru Nica

Download or read book Lectures on the Combinatorics of Free Probability written by Alexandru Nica and published by Cambridge University Press. This book was released on 2006-09-07 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2006 book is a self-contained introduction to free probability theory suitable for an introductory graduate level course.

Selected Papers on Classical Analysis

Author : 野水克己
Publisher : American Mathematical Soc.
ISBN 13 : 9780821827802
Total Pages : 148 pages
Book Rating : 4.8/5 (278 download)

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Book Synopsis Selected Papers on Classical Analysis by : 野水克己

Download or read book Selected Papers on Classical Analysis written by 野水克己 and published by American Mathematical Soc.. This book was released on 2001 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers that originally appeared in Japanese in the journal Sugaku. Ordinarily the papers would appear in the AMS translation of that journal, but to expedite publication, the Society has chosen to publish them as a volume of selected papers. The papers here are in the general area of mathematical analysis as it pertains to free probability theory.

Complex Function Theory, Operator Theory, Schur Analysis and Systems Theory

Author : Daniel Alpay
Publisher : Springer Nature
ISBN 13 : 3030448193
Total Pages : 578 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Complex Function Theory, Operator Theory, Schur Analysis and Systems Theory by : Daniel Alpay

Download or read book Complex Function Theory, Operator Theory, Schur Analysis and Systems Theory written by Daniel Alpay and published by Springer Nature. This book was released on 2020-09-19 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is dedicated to Victor Emmanuilovich Katsnelson on the occasion of his 75th birthday and celebrates his broad mathematical interests and contributions.Victor Emmanuilovich’s mathematical career has been based mainly at the Kharkov University and the Weizmann Institute. However, it also included a one-year guest professorship at Leipzig University in 1991, which led to him establishing close research contacts with the Schur analysis group in Leipzig, a collaboration that still continues today. Reflecting these three periods in Victor Emmanuilovich's career, present and former colleagues have contributed to this book with research inspired by him and presentations on their joint work. Contributions include papers in function theory (Favorov-Golinskii, Friedland-Goldman-Yomdin, Kheifets-Yuditskii) , Schur analysis, moment problems and related topics (Boiko-Dubovoy, Dyukarev, Fritzsche-Kirstein-Mädler), extension of linear operators and linear relations (Dijksma-Langer, Hassi-de Snoo, Hassi -Wietsma) and non-commutative analysis (Ball-Bolotnikov, Cho-Jorgensen).

Topological and Asymptotic Aspects of Group Theory

Author : R. I. Grigorchuk
Publisher : American Mathematical Soc.
ISBN 13 : 0821837567
Total Pages : 248 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topological and Asymptotic Aspects of Group Theory by : R. I. Grigorchuk

Download or read book Topological and Asymptotic Aspects of Group Theory written by R. I. Grigorchuk and published by American Mathematical Soc.. This book was released on 2006 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume are based on the talks given at two special sessions at the AMS Sectional meetings held in 2004. The articles cover various topological and asymptotic aspects of group theory, such as hyperbolic and relatively hyperbolic groups, asymptotic cones, Thompson's group, Nielsen fixed point theory, homology, groups acting on trees, groups generated by finite automata, iterated monodromy groups, random walks on finitely generated groups, heat kernels, and currents on free groups.

Proceedings of the Conference Quantum Probability and Infinite Dimensional Analysis

Author : Wolfgang Freudenberg
Publisher : World Scientific
ISBN 13 : 9812382887
Total Pages : 277 pages
Book Rating : 4.8/5 (123 download)

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Book Synopsis Proceedings of the Conference Quantum Probability and Infinite Dimensional Analysis by : Wolfgang Freudenberg

Download or read book Proceedings of the Conference Quantum Probability and Infinite Dimensional Analysis written by Wolfgang Freudenberg and published by World Scientific. This book was released on 2003 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of 18 research papers reflecting the impressive progress made in the field. It includes new results on quantum stochastic integration, the stochastic limit, quantum teleportation and other areas. Contents: Markov Property -- Recent Developments on the Quantum Markov Property (L Accardi & F Fidaleo); Stationary Quantum Stochastic Processes from the Cohomological Point of View (G G Amosov); The Feller Property of a Class of Quantum Markov Semigroups II (R Carbone & F Fagnola); Recognition and Teleportation (K-H Fichtner et al.); Prediction Errors and Completely Positive Maps (R Gohm); Multiplicative Properties of Double Stochastic Product Integrals (R L Hudson); Isometric Cocycles Related to Beam Splittings (V Liebscher); Multiplicativity via a Hat Trick (J M Lindsay & S J Wills); Dilation Theory and Continuous Tensor Product Systems of Hilbert Modules (M Skeide); Quasi-Free Fermion Planar Quantum Stochastic Integrals (W J Spring & I F Wilde); and other papers.

Quantum Probability and Infinite-Dimensional Analysis

Author :
Publisher :
ISBN 13 : 9814486566
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Quantum Probability and Infinite-Dimensional Analysis by :

Download or read book Quantum Probability and Infinite-Dimensional Analysis written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Encyclopedia of Nonlinear Science

Author : Alwyn Scott
Publisher : Routledge
ISBN 13 : 1135455570
Total Pages : 2881 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Encyclopedia of Nonlinear Science by : Alwyn Scott

Download or read book Encyclopedia of Nonlinear Science written by Alwyn Scott and published by Routledge. This book was released on 2006-05-17 with total page 2881 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.

Quantum Probability and Spectral Analysis of Graphs

Author : Akihito Hora
Publisher : Springer Science & Business Media
ISBN 13 : 3540488634
Total Pages : 384 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Quantum Probability and Spectral Analysis of Graphs by : Akihito Hora

Download or read book Quantum Probability and Spectral Analysis of Graphs written by Akihito Hora and published by Springer Science & Business Media. This book was released on 2007-07-05 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to comprehensively cover quantum probabilistic approaches to spectral analysis of graphs, an approach developed by the authors. The book functions as a concise introduction to quantum probability from an algebraic aspect. Here readers will learn several powerful methods and techniques of wide applicability, recently developed under the name of quantum probability. The exercises at the end of each chapter help to deepen understanding.

The Semicircle Law, Free Random Variables and Entropy

Author : Fumio Hiai
Publisher : American Mathematical Soc.
ISBN 13 : 0821841351
Total Pages : 389 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Semicircle Law, Free Random Variables and Entropy by : Fumio Hiai

Download or read book The Semicircle Law, Free Random Variables and Entropy written by Fumio Hiai and published by American Mathematical Soc.. This book was released on 2000 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book treats free probability theory, which has been extensively developed since the early 1980s. The emphasis is put on entropy and the random matrix model approach. The volume is a unique presentation demonstrating the extensive interrelation between the topics. Wigner's theorem and its broad generalizations, such as asymptotic freeness of independent matrices, are explained in detail. Consistent throughout the book is the parallelism between the normal and semicircle laws. Voiculescu's multivariate free entropy theory is presented with full proofs and extends the results to unitary operators. Some applications to operator algebras are also given. Based on lectures given by the authors in Hungary, Japan, and Italy, the book is a good reference for mathematicians interested in free probability theory and can serve as a text for an advanced graduate course. This book brings together both new material and recent surveys on some topics in differential equations that are either directly relevant to, or closely associated with, mathematical physics. Its topics include asymptotic formulas for the ground-state energy of fermionic gas, renormalization ideas in quantum field theory from perturbations of the free Hamiltonian on the circle, $J$-selfadjoint Dirac operators, spectral theory of Schrodinger operators, inverse problems, isoperimetric inequalities in quantum mechanics, Hardy inequalities, and non-adiabatic transitions. Excellent survey articles on Dirichlet-Neumann inverse problems on manifolds (by Uhlmann), numerical investigations associated with Laplacian eigenvalues on planar regions (by Trefethen), Snell's law and propagation of singularities in the wave equation (by Vasy), random operators on tree graphs (by Aizenmann) make this book interesting and valuable for graduate students, young mathematicians, and physicists alike.

Algebras, Graphs and their Applications

Author : Ilwoo Cho
Publisher : CRC Press
ISBN 13 : 146659019X
Total Pages : 446 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Algebras, Graphs and their Applications by : Ilwoo Cho

Download or read book Algebras, Graphs and their Applications written by Ilwoo Cho and published by CRC Press. This book was released on 2013-09-11 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the study of algebra induced by combinatorial objects called directed graphs. These graphs are used as tools in the analysis of graph-theoretic problems and in the characterization and solution of analytic problems. The book presents recent research in operator algebra theory connected with discrete and combinatorial mathematical objects. It also covers tools and methods from a variety of mathematical areas, including algebra, operator theory, and combinatorics, and offers numerous applications of fractal theory, entropy theory, K-theory, and index theory.

Commutative and Noncommutative Harmonic Analysis and Applications

Author : Azita Mayeli
Publisher : American Mathematical Soc.
ISBN 13 : 0821894935
Total Pages : 218 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Commutative and Noncommutative Harmonic Analysis and Applications by : Azita Mayeli

Download or read book Commutative and Noncommutative Harmonic Analysis and Applications written by Azita Mayeli and published by American Mathematical Soc.. This book was released on 2013-11-08 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Wavelet and Frame Theoretic Methods in Harmonic Analysis and Partial Differential Equations, held September 22-23, 2012, at the Rochester Institute of Technology, Rochester, NY, USA. The book features new directions, results and ideas in commutative and noncommutative abstract harmonic analysis, operator theory and applications. The commutative part includes shift invariant spaces, abelian group action on Euclidean space and frame theory; the noncommutative part includes representation theory, continuous and discrete wavelets related to four dimensional Euclidean space, frames on symmetric spaces, $C DEGREES*$-algebras, projective multiresolutions, and free probability algebras. The scope of the book goes beyond traditional harmonic analysis, dealing with Fourier tools, transforms, Fourier bases, and associated function spaces. A number of papers take the step toward wavelet analysis, and even more general tools for analysis/synthesis problems, including papers on frames (over-complete bases) and their practical applications to engineering, cosmology and astrophysics.Other applications in this book include explicit families of wavelets and frames, as they are used in signal processing, multiplexing, and the study of Cosmic Microwave Background (CMB) radiation. For the purpose of organisation, the book is divided into three parts: noncommutative, commutative, and applications. The first group of papers are devoted to problems in noncommutative harmonic analysis, the second to topics in commutative harmonic analysis, and the third to such applications as wavelet and frame theory and to some real-world applications.

Recent Developments in Stochastic Analysis and Related Topics

Author : Sergio Albeverio
Publisher : World Scientific
ISBN 13 : 9812561048
Total Pages : 471 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Recent Developments in Stochastic Analysis and Related Topics by : Sergio Albeverio

Download or read book Recent Developments in Stochastic Analysis and Related Topics written by Sergio Albeverio and published by World Scientific. This book was released on 2004 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains 27 refereed research articles and survey papers written by experts in the field of stochastic analysis and related topics. Most contributors are well known leading mathematicians worldwide and prominent young scientists. The volume reflects a review of the recent developments in stochastic analysis and related topics. It puts in evidence the strong interconnection of stochastic analysis with other areas of mathematics, as well as with applications of mathematics in natural and social economic sciences. The volume also provides some possible future directions for the field.The proceedings have been selected for coverage in: ? Index to Scientific & Technical Proceedings? (ISTP? / ISI Proceedings)? Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)? CC Proceedings ? Engineering & Physical Sciences

Free Probability Theory

Author : Dan V. Voiculescu
Publisher : American Mathematical Soc.
ISBN 13 : 0821806750
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Free Probability Theory by : Dan V. Voiculescu

Download or read book Free Probability Theory written by Dan V. Voiculescu and published by American Mathematical Soc.. This book was released on 1997 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Probability on Algebraic Structures

Author : Gregory Budzban
Publisher : American Mathematical Soc.
ISBN 13 : 0821820273
Total Pages : 250 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Probability on Algebraic Structures by : Gregory Budzban

Download or read book Probability on Algebraic Structures written by Gregory Budzban and published by American Mathematical Soc.. This book was released on 2000 with total page 250 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents results from an AMS Special Session held on the topic in Gainesville (FL). Papers included are written by an international group of well-known specialists who offer an important cross-section of current work in the field. In addition there are two expository papers that provide an avenue for non-specialists to comprehend problems in this area. The breadth of research in this area is evident by the variety of articles presented in the volume. Results concern probability on Lie groups and general locally compact groups. Generalizations of groups appear as hypergroups, abstract semigroups, and semigroups of matrices. Work on symmetric cones is included. Lastly, there are a number of articles on the current progress in constructing stochastic processes on quantum groups.