Download or read book Spectral Theory Of Large Dimensional Random Matrices And Its Applications To Wireless Communications And Finance Statistics Random Matrix Theory And Its Applications written by Zhaoben Fang and published by World Scientific. This book was released on 2014-01-24 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spectral Analysis of Large Dimensional Random Matrices written by Zhidong Bai and published by Springer Science & Business Media. This book was released on 2009-12-10 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Data Centric Business and Applications written by Dmytro Ageyev and published by Springer Nature. This book was released on 2021-06-04 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, building on the authors’ previous work, presents new communication and networking technologies, challenges and opportunities of information/data processing and transmission. It also discusses the development of more intelligent and efficient communication technologies, which are an essential part of current day-to-day life. Information and Communication Technologies (ICTs) have an enormous impact on businesses and our day-to-day lives over the past three decades and continue to do so. Modern methods of business information processing are opening exciting new opportunities for doing business on the basis of information technologies. The book contains research that spans a wide range of communication and networking technologies, including wireless sensor networks, optical and telecommunication networks, storage area networks, error-free transmission and signal processing.
Download or read book Deep Learning Techniques and Optimization Strategies in Big Data Analytics written by Thomas, J. Joshua and published by IGI Global. This book was released on 2019-11-29 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many approaches have sprouted from artificial intelligence (AI) and produced major breakthroughs in the computer science and engineering industries. Deep learning is a method that is transforming the world of data and analytics. Optimization of this new approach is still unclear, however, and there’s a need for research on the various applications and techniques of deep learning in the field of computing. Deep Learning Techniques and Optimization Strategies in Big Data Analytics is a collection of innovative research on the methods and applications of deep learning strategies in the fields of computer science and information systems. While highlighting topics including data integration, computational modeling, and scheduling systems, this book is ideally designed for engineers, IT specialists, data analysts, data scientists, engineers, researchers, academicians, and students seeking current research on deep learning methods and its application in the digital industry.
Download or read book Multi Objective Optimization of Industrial Power Generation Systems Emerging Research and Opportunities written by Ganesan, Timothy and published by IGI Global. This book was released on 2019-12-27 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: The increased complexity of the economy in recent years has led to the advancement of energy generation systems. Engineers in this industrial sector have been compelled to seek contemporary methods to keep pace with the rapid development of these systems. Computational intelligence has risen as a capable method that can effectively resolve complex scenarios within the power generation sector. In-depth research on the various applications of this technology is lacking, as engineering professionals need up-to-date information on how to successfully utilize computational intelligence in industrial systems. Multi-Objective Optimization of Industrial Power Generation Systems: Emerging Research and Opportunities provides emerging research exploring the theoretical and practical aspects of the application of intelligent optimization techniques within industrial energy systems. Featuring coverage on a broad range of topics such as swarm intelligence, renewable energy, and predictive modeling, this book is ideally designed for industrialists, engineers, industry professionals, researchers, students, and academics seeking current research on computational intelligence frameworks within the power generation sector.
Download or read book A Concise Text on Advanced Linear Algebra written by Yisong Yang and published by Cambridge University Press. This book was released on 2015 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: This engaging, well-motivated textbook helps advanced undergraduate students to grasp core concepts and reveals applications in mathematics and beyond.
Download or read book Smart Grid using Big Data Analytics written by Robert C. Qiu and published by John Wiley & Sons. This book was released on 2017-04-17 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Random Matrices High Dimensional Phenomena written by Gordon Blower and published by Cambridge University Press. This book was released on 2009-10-08 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium.
Download or read book An Introduction to Matrix Concentration Inequalities written by Joel Tropp and published by . This book was released on 2015-05-27 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Random Matrices and Their Applications written by Joel E. Cohen and published by American Mathematical Soc.. This book was released on 1986 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features twenty-six expository papers on random matrices and products of random matrices. This work reflects both theoretical and applied concerns in fields as diverse as computer science, probability theory, mathematical physics, and population biology.
Download or read book A First Course in Random Matrix Theory written by Marc Potters and published by Cambridge University Press. This book was released on 2020-12-03 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.
Download or read book Random Matrix Theory and Its Application in High dimensional Statistics written by Danning Li and published by . This book was released on 2013 with total page 124 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 343 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.
Download or read book Introduction to Random Matrices written by Giacomo Livan and published by Springer. This book was released on 2018-01-16 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum.The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory).Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.
Download or read book Eigenvalue Distribution of Large Random Matrices written by Leonid Andreevich Pastur and published by American Mathematical Soc.. This book was released on 2011 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries). The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes. This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.
Download or read book Applications of Random Matrices in Physics written by Édouard Brezin and published by Springer Science & Business Media. This book was released on 2006-07-03 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.
Download or read book Spectral Theory of Random Matrices written by Vyacheslav L. Girko and published by Academic Press. This book was released on 2016-08-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Theory of Random Matrices
