The Semicircle Law Free Random Variables And Entropy
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The Semicircle Law Free Random Variables And Entropy
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Author : Fumio Hiai
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
The Semicircle Law Free Random Variables And Entropy written by Fumio Hiai and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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.
An Introduction To Random Matrices
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Author : Greg W. Anderson
language : en
Publisher: Cambridge University Press
Release Date : 2010
An Introduction To Random Matrices written by Greg W. Anderson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.
Mathematical Foundations For Signal Processing Communications And Networking
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Author : Erchin Serpedin
language : en
Publisher: CRC Press
Release Date : 2017-12-04
Mathematical Foundations For Signal Processing Communications And Networking written by Erchin Serpedin and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-04 with Computers categories.
Mathematical Foundations for Signal Processing, Communications, and Networking describes mathematical concepts and results important in the design, analysis, and optimization of signal processing algorithms, modern communication systems, and networks. Helping readers master key techniques and comprehend the current research literature, the book offers a comprehensive overview of methods and applications from linear algebra, numerical analysis, statistics, probability, stochastic processes, and optimization. From basic transforms to Monte Carlo simulation to linear programming, the text covers a broad range of mathematical techniques essential to understanding the concepts and results in signal processing, telecommunications, and networking. Along with discussing mathematical theory, each self-contained chapter presents examples that illustrate the use of various mathematical concepts to solve different applications. Each chapter also includes a set of homework exercises and readings for additional study. This text helps readers understand fundamental and advanced results as well as recent research trends in the interrelated fields of signal processing, telecommunications, and networking. It provides all the necessary mathematical background to prepare students for more advanced courses and train specialists working in these areas.
Random Matrix Methods For Wireless Communications
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Author : Romain Couillet
language : en
Publisher: Cambridge University Press
Release Date : 2011-09-29
Random Matrix Methods For Wireless Communications written by Romain Couillet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-29 with Technology & Engineering categories.
Blending theoretical results with practical applications, this book provides an introduction to random matrix theory and shows how it can be used to tackle a variety of problems in wireless communications. The Stieltjes transform method, free probability theory, combinatoric approaches, deterministic equivalents and spectral analysis methods for statistical inference are all covered from a unique engineering perspective. Detailed mathematical derivations are presented throughout, with thorough explanation of the key results and all fundamental lemmas required for the reader to derive similar calculus on their own. These core theoretical concepts are then applied to a wide range of real-world problems in signal processing and wireless communications, including performance analysis of CDMA, MIMO and multi-cell networks, as well as signal detection and estimation in cognitive radio networks. The rigorous yet intuitive style helps demonstrate to students and researchers alike how to choose the correct approach for obtaining mathematically accurate results.
Random Matrix Theory And Its Applications Multivariate Statistics And Wireless Communications
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Author : Zhidong Bai
language : en
Publisher: World Scientific
Release Date : 2009-07-27
Random Matrix Theory And Its Applications Multivariate Statistics And Wireless Communications written by Zhidong Bai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-27 with Mathematics categories.
Random matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of the energy levels of heavy nuclei. The subject was further deeply developed under the important leadership of Dyson, Gaudin and Mehta, and other mathematical physicists.In the early 1990s, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, the subject has seen applications in such diverse areas as large dimensional data analysis and wireless communications.This volume contains chapters written by the leading participants in the field which will serve as a valuable introduction into this very exciting area of research.
Bayesian Probability Theory
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Author : Wolfgang von der Linden
language : en
Publisher: Cambridge University Press
Release Date : 2014-06-12
Bayesian Probability Theory written by Wolfgang von der Linden and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-12 with Mathematics categories.
Covering all aspects of probability theory, statistics and data analysis from a Bayesian perspective for graduate students and researchers.
Random Matrix Methods For Machine Learning
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Author : Romain Couillet
language : en
Publisher: Cambridge University Press
Release Date : 2022-07-21
Random Matrix Methods For Machine Learning written by Romain Couillet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-21 with Computers categories.
This unified random matrix approach to large-dimensional machine learning covers applications from power detection to deep neural networks.
Smart Grid Using Big Data Analytics
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Author : Robert C. Qiu
language : en
Publisher: John Wiley & Sons
Release Date : 2017-01-23
Smart Grid Using Big Data Analytics written by Robert C. Qiu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-23 with Technology & Engineering categories.
This book is aimed at students in communications and signal processing who want to extend their skills in the energy area. It describes power systems and why these backgrounds are so useful to smart grid, wireless communications being very different to traditional wireline communications.
Cognitive Radio Communication And Networking
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Author : Robert Caiming Qiu
language : en
Publisher: John Wiley & Sons
Release Date : 2012-09-10
Cognitive Radio Communication And Networking written by Robert Caiming Qiu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-10 with Technology & Engineering categories.
The author presents a unified treatment of this highly interdisciplinary topic to help define the notion of cognitive radio. The book begins with addressing issues such as the fundamental system concept and basic mathematical tools such as spectrum sensing and machine learning, before moving on to more advanced concepts and discussions about the future of cognitive radio. From the fundamentals in spectrum sensing to the applications of cognitive algorithms to radio communications, and discussion of radio platforms and testbeds to show the applicability of the theory to practice, the author aims to provide an introduction to a fast moving topic for students and researchers seeking to develop a thorough understanding of cognitive radio networks. Examines basic mathematical tools before moving on to more advanced concepts and discussions about the future of cognitive radio Describe the fundamentals of cognitive radio, providing a step by step treatment of the topics to enable progressive learning Includes questions, exercises and suggestions for extra reading at the end of each chapter Topics covered in the book include: Spectrum Sensing: Basic Techniques; Cooperative Spectrum Sensing Wideband Spectrum Sensing; Agile Transmission Techniques: Orthogonal Frequency Division Multiplexing Multiple Input Multiple Output for Cognitive Radio; Convex Optimization for Cognitive Radio; Cognitive Core (I): Algorithms for Reasoning and Learning; Cognitive Core (II): Game Theory; Cognitive Radio Network IEEE 802.22: The First Cognitive Radio Wireless Regional Area Network Standard, and Radio Platforms and Testbeds.
Hypercomplex Analysis New Perspectives And Applications
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Author : Swanhild Bernstein
language : en
Publisher: Springer
Release Date : 2014-10-10
Hypercomplex Analysis New Perspectives And Applications written by Swanhild Bernstein and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-10 with Mathematics categories.
Hypercomplex analysis is the extension of complex analysis to higher dimensions where the concept of a holomorphic function is substituted by the concept of a monogenic function. In recent decades this theory has come to the forefront of higher dimensional analysis. There are several approaches to this: quaternionic analysis which merely uses quaternions, Clifford analysis which relies on Clifford algebras, and generalizations of complex variables to higher dimensions such as split-complex variables. This book includes a selection of papers presented at the session on quaternionic and hypercomplex analysis at the ISAAC conference 2013 in Krakow, Poland. The topics covered represent new perspectives and current trends in hypercomplex analysis and applications to mathematical physics, image analysis and processing, and mechanics.