Random Matrix Theory And Its Applications Multivariate Statistics And Wireless Communications PDF Download
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Author | : Zhidong Bai |
Publisher | : World Scientific |
Total Pages | : 176 |
Release | : 2009-07-27 |
Genre | : Mathematics |
ISBN | : 9814467995 |
Download Random Matrix Theory And Its Applications: Multivariate Statistics And Wireless Communications Book in PDF, ePub and Kindle
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.
Author | : Antonia M. Tulino |
Publisher | : Now Publishers Inc |
Total Pages | : 196 |
Release | : 2004 |
Genre | : Computers |
ISBN | : 9781933019000 |
Download Random Matrix Theory and Wireless Communications Book in PDF, ePub and Kindle
Random Matrix Theory and Wireless Communications is the first tutorial on random matrices which provides an overview of the theory and brings together in one source the most significant results recently obtained.
Author | : Zhaoben Fang |
Publisher | : World Scientific |
Total Pages | : 233 |
Release | : 2014-01-24 |
Genre | : Mathematics |
ISBN | : 9814579076 |
Download Spectral Theory Of Large Dimensional Random Matrices And Its Applications To Wireless Communications And Finance Statistics: Random Matrix Theory And Its Applications Book in PDF, ePub and Kindle
The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance.
Author | : Zhidong Bai |
Publisher | : Springer Science & Business Media |
Total Pages | : 560 |
Release | : 2009-12-10 |
Genre | : Mathematics |
ISBN | : 1441906614 |
Download Spectral Analysis of Large Dimensional Random Matrices Book in PDF, ePub and Kindle
The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science. The book introduces fundamental results, most of them investigated by the authors, such as the semicircular law of Wigner matrices, the Marcenko-Pastur law, the limiting spectral distribution of the multivariate F matrix, limits of extreme eigenvalues, spectrum separation theorems, convergence rates of empirical distributions, central limit theorems of linear spectral statistics, and the partial solution of the famous circular law. While deriving the main results, the book simultaneously emphasizes the ideas and methodologies of the fundamental mathematical tools, among them being: truncation techniques, matrix identities, moment convergence theorems, and the Stieltjes transform. Its treatment is especially fitting to the needs of mathematics and statistics graduate students and beginning researchers, having a basic knowledge of matrix theory and an understanding of probability theory at the graduate level, who desire to learn the concepts and tools in solving problems in this area. It can also serve as a detailed handbook on results of large dimensional random matrices for practical users. This second edition includes two additional chapters, one on the authors' results on the limiting behavior of eigenvectors of sample covariance matrices, another on applications to wireless communications and finance. While attempting to bring this edition up-to-date on recent work, it also provides summaries of other areas which are typically considered part of the general field of random matrix theory.
Author | : Romain Couillet |
Publisher | : |
Total Pages | : 539 |
Release | : 2011 |
Genre | : Matrix analytic methods |
ISBN | : 9781139139601 |
Download Random Matrix Methods for Wireless Communications Book in PDF, ePub and Kindle
"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"--
Author | : Romain Couillet |
Publisher | : |
Total Pages | : 563 |
Release | : 2014-05-14 |
Genre | : Matrix analytic methods |
ISBN | : 9781139145381 |
Download Random Matrix Methods for Wireless Communications Book in PDF, ePub and Kindle
An introduction to random matrix theory and its applications to real-world problems in signal processing and wireless communications.
Author | : Gernot Akemann |
Publisher | : Oxford Handbooks |
Total Pages | : 0 |
Release | : 2015-08-09 |
Genre | : Mathematics |
ISBN | : 9780198744191 |
Download The Oxford Handbook of Random Matrix Theory Book in PDF, ePub and Kindle
With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach.In part one, all modern and classical techniques of solving random matrix models are explored, including orthogonal polynomials, exact replicas or supersymmetry.
Author | : Pavel Bleher |
Publisher | : Cambridge University Press |
Total Pages | : 454 |
Release | : 2001-06-04 |
Genre | : Mathematics |
ISBN | : 9780521802093 |
Download Random Matrix Models and Their Applications Book in PDF, ePub and Kindle
Expository articles on random matrix theory emphasizing the exchange of ideas between the physical and mathematical communities.
Author | : Joel Tropp |
Publisher | : |
Total Pages | : 256 |
Release | : 2015-05-27 |
Genre | : Computers |
ISBN | : 9781601988386 |
Download An Introduction to Matrix Concentration Inequalities Book in PDF, ePub and Kindle
Random matrices now play a role in many areas of theoretical, applied, and computational mathematics. It is therefore desirable to have tools for studying random matrices that are flexible, easy to use, and powerful. Over the last fifteen years, researchers have developed a remarkable family of results, called matrix concentration inequalities, that achieve all of these goals. This monograph offers an invitation to the field of matrix concentration inequalities. It begins with some history of random matrix theory; it describes a flexible model for random matrices that is suitable for many problems; and it discusses the most important matrix concentration results. To demonstrate the value of these techniques, the presentation includes examples drawn from statistics, machine learning, optimization, combinatorics, algorithms, scientific computing, and beyond.
Author | : Elizabeth S. Meckes |
Publisher | : Cambridge University Press |
Total Pages | : 225 |
Release | : 2019-08-01 |
Genre | : Mathematics |
ISBN | : 1108317995 |
Download The Random Matrix Theory of the Classical Compact Groups Book in PDF, ePub and Kindle
This is the first book to provide a comprehensive overview of foundational results and recent progress in the study of random matrices from the classical compact groups, drawing on the subject's deep connections to geometry, analysis, algebra, physics, and statistics. The book sets a foundation with an introduction to the groups themselves and six different constructions of Haar measure. Classical and recent results are then presented in a digested, accessible form, including the following: results on the joint distributions of the entries; an extensive treatment of eigenvalue distributions, including the Weyl integration formula, moment formulae, and limit theorems and large deviations for the spectral measures; concentration of measure with applications both within random matrix theory and in high dimensional geometry; and results on characteristic polynomials with connections to the Riemann zeta function. This book will be a useful reference for researchers and an accessible introduction for students in related fields.