Random Circulant Matrices

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Random Circulant Matrices

Arup Bose,Koushik Saha
Random Circulant Matrices Book PDF

Author : Arup Bose,Koushik Saha
Publisher : CRC Press
Page : 192 pages
File Size : 48,7 Mb
Release : 2018-11-05
Category : Mathematics
ISBN : 9780429788192

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Random Circulant Matrices by Arup Bose,Koushik Saha Pdf

Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k-circulant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and are light- or heavy-tailed. Arup Bose obtained his B.Stat., M.Stat. and Ph.D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit, Kolkata, India since 1991. He is a Fellow of the Institute of Mathematical Statistics, and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is the author of three books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and U-Statistics, M_m-Estimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B.Sc. in Mathematics from Ramakrishna Mission Vidyamandiara, Belur and an M.Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph.D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics, Indian Institute of Technology Bombay since 2014.

Random Circulant Matrices

Arup Bose,Koushik Saha
Random Circulant Matrices Book PDF

Author : Arup Bose,Koushik Saha
Publisher : CRC Press
Page : 98 pages
File Size : 40,7 Mb
Release : 2018-11-05
Category : Mathematics
ISBN : 9780429788185

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Random Circulant Matrices by Arup Bose,Koushik Saha Pdf

Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k-circulant when the dimension of the matrices grow and the entries are random. In particular, the behavior of the spectral distribution, of the spectral radius and of the appropriate point processes are developed systematically using the method of moments and the various powerful normal approximation results. This behavior varies according as the entries are independent, are from a linear process, and are light- or heavy-tailed. Arup Bose obtained his B.Stat., M.Stat. and Ph.D. degrees from the Indian Statistical Institute. He has been on its faculty at the Theoretical Statistics and Mathematics Unit, Kolkata, India since 1991. He is a Fellow of the Institute of Mathematical Statistics, and of all three national science academies of India. He is a recipient of the S.S. Bhatnagar Prize and the C.R. Rao Award. He is the author of three books: Patterned Random Matrices, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee) and U-Statistics, M_m-Estimators and Resampling (with Snigdhansu Chatterjee). Koushik Saha obtained a B.Sc. in Mathematics from Ramakrishna Mission Vidyamandiara, Belur and an M.Sc. in Mathematics from Indian Institute of Technology Bombay. He obtained his Ph.D. degree from the Indian Statistical Institute under the supervision of Arup Bose. His thesis on circulant matrices received high praise from the reviewers. He has been on the faculty of the Department of Mathematics, Indian Institute of Technology Bombay since 2014.

Toeplitz and Circulant Matrices

Robert M. Gray
Toeplitz and Circulant Matrices Book PDF

Author : Robert M. Gray
Publisher : Now Publishers Inc
Page : 105 pages
File Size : 51,9 Mb
Release : 2006
Category : Computers
ISBN : 9781933019239

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Toeplitz and Circulant Matrices by Robert M. Gray Pdf

The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes. The fundamental theorems on the asymptotic behavior of eigenvalues, inverses, and products of banded Toeplitz matrices and Toeplitz matrices with absolutely summable elements are derived in a tutorial manner. Mathematical elegance and generality are sacrificed for conceptual simplicity and insight in the hope of making these results available to engineers lacking either the background or endurance to attack the mathematical literature on the subject. By limiting the generality of the matrices considered, the essential ideas and results can be conveyed in a more intuitive manner without the mathematical machinery required for the most general cases. As an application the results are applied to the study of the covariance matrices and their factors of linear models of discrete time random processes.

Patterned Random Matrices

Arup Bose
Patterned Random Matrices Book PDF

Author : Arup Bose
Publisher : CRC Press
Page : 269 pages
File Size : 47,5 Mb
Release : 2018-05-23
Category : Mathematics
ISBN : 9780429948893

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Patterned Random Matrices by Arup Bose Pdf

Large dimensional random matrices (LDRM) with specific patterns arise in econometrics, computer science, mathematics, physics, and statistics. This book provides an easy initiation to LDRM. Through a unified approach, we investigate the existence and properties of the limiting spectral distribution (LSD) of different patterned random matrices as the dimension grows. The main ingredients are the method of moments and normal approximation with rudimentary combinatorics for support. Some elementary results from matrix theory are also used. By stretching the moment arguments, we also have a brush with the intriguing but difficult concepts of joint convergence of sequences of random matrices and its ramifications. This book covers the Wigner matrix, the sample covariance matrix, the Toeplitz matrix, the Hankel matrix, the sample autocovariance matrix and the k-Circulant matrices. Quick and simple proofs of their LSDs are provided and it is shown how the semi-circle law and the March enko-Pastur law arise as the LSDs of the first two matrices. Extending the basic approach, we also establish interesting limits for some triangular matrices, band matrices, balanced matrices, and the sample autocovariance matrix. We also study the joint convergence of several patterned matrices, and show that independent Wigner matrices converge jointly and are asymptotically free of other patterned matrices. Arup Bose is a Professor at the Indian Statistical Institute, Kolkata, India. He is a distinguished researcher in Mathematical Statistics and has been working in high-dimensional random matrices for the last fifteen years. He has been the Editor of Sankyhā for several years and has been on the editorial board of several other journals. He is a Fellow of the Institute of Mathematical Statistics, USA and all three national science academies of India, as well as the recipient of the S.S. Bhatnagar Award and the C.R. Rao Award. His forthcoming books are the monograph, Large Covariance and Autocovariance Matrices (with Monika Bhattacharjee), to be published by Chapman & Hall/CRC Press, and a graduate text, U-statistics, M-estimates and Resampling (with Snigdhansu Chatterjee), to be published by Hindustan Book Agency.

Random Matrices and Non-Commutative Probability

Arup Bose
Random Matrices and Non Commutative Probability Book PDF

Author : Arup Bose
Publisher : CRC Press
Page : 287 pages
File Size : 55,9 Mb
Release : 2021-10-26
Category : Mathematics
ISBN : 9781000458817

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Random Matrices and Non-Commutative Probability by Arup Bose Pdf

This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Möbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.

Introduction to Random Matrices

Giacomo Livan,Marcel Novaes,Pierpaolo Vivo
Introduction to Random Matrices Book PDF

Author : Giacomo Livan,Marcel Novaes,Pierpaolo Vivo
Publisher : Springer
Page : 124 pages
File Size : 45,5 Mb
Release : 2018-01-16
Category : Science
ISBN : 9783319708850

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Introduction to Random Matrices by Giacomo Livan,Marcel Novaes,Pierpaolo Vivo Pdf

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.

An Introduction to Random Matrices

Greg W. Anderson,Alice Guionnet,Ofer Zeitouni
An Introduction to Random Matrices Book PDF

Author : Greg W. Anderson,Alice Guionnet,Ofer Zeitouni
Publisher : Cambridge University Press
Page : 507 pages
File Size : 50,5 Mb
Release : 2010
Category : Mathematics
ISBN : 9780521194525

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An Introduction to Random Matrices by Greg W. Anderson,Alice Guionnet,Ofer Zeitouni Pdf

A rigorous introduction to the basic theory of random matrices designed for graduate students with a background in probability theory.

Compressive Sensing for Wireless Communication

Radha Sankararajan,Hemalatha Rajendran,Aasha Nandhini Sukumaran
Compressive Sensing for Wireless Communication Book PDF

Author : Radha Sankararajan,Hemalatha Rajendran,Aasha Nandhini Sukumaran
Publisher : CRC Press
Page : 493 pages
File Size : 40,9 Mb
Release : 2022-09-01
Category : Technology & Engineering
ISBN : 9781000794366

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Compressive Sensing for Wireless Communication by Radha Sankararajan,Hemalatha Rajendran,Aasha Nandhini Sukumaran Pdf

Compressed Sensing (CS) is a promising method that recovers the sparse and compressible signals from severely under-sampled measurements. CS can be applied to wireless communication to enhance its capabilities. As this technology is proliferating, it is possible to explore its need and benefits for emerging applicationsCompressive Sensing for Wireless Communication provides:• A clear insight into the basics of compressed sensing• A thorough exploration of applying CS to audio, image and computer vision• Different dimensions of applying CS in Cognitive radio networks• CS in wireless sensor network for spatial compression and projection• Real world problems/projects that can be implemented and tested• Efficient methods to sample and reconstruct the images in resource constrained WMSN environmentThis book provides the details of CS and its associated applications in a thorough manner. It lays a direction for students and new engineers and prepares them for developing new tasks within the field of CS. It is an indispensable companion for practicing engineers who wish to learn about the emerging areas of interest.

Random Matrices and Non-Commutative Probability

Arup Bose
Random Matrices and Non Commutative Probability Book PDF

Author : Arup Bose
Publisher : CRC Press
Page : 420 pages
File Size : 47,7 Mb
Release : 2021-10-26
Category : Mathematics
ISBN : 9781000458824

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Random Matrices and Non-Commutative Probability by Arup Bose Pdf

This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The book assumes almost no prerequisite for the most part. However, familiarity with the basic convergence concepts in probability and a bit of mathematical maturity will be helpful. Combinatorial properties of non-crossing partitions, including the Möbius function play a central role in introducing free probability. Free independence is defined via free cumulants in analogy with the way classical independence can be defined via classical cumulants. Free cumulants are introduced through the Möbius function. Free product probability spaces are constructed using free cumulants. Marginal and joint tracial convergence of large dimensional random matrices such as the Wigner, elliptic, sample covariance, cross-covariance, Toeplitz, Circulant and Hankel are discussed. Convergence of the empirical spectral distribution is discussed for symmetric matrices. Asymptotic freeness results for random matrices, including some recent ones, are discussed in detail. These clarify the structure of the limits for joint convergence of random matrices. Asymptotic freeness of independent sample covariance matrices is also demonstrated via embedding into Wigner matrices. Exercises, at advanced undergraduate and graduate level, are provided in each chapter.

Random Matrices

Alexei Borodin,Ivan Corwin,Alice Guionnet
Random Matrices Book PDF

Author : Alexei Borodin,Ivan Corwin,Alice Guionnet
Publisher : American Mathematical Soc.
Page : 498 pages
File Size : 43,9 Mb
Release : 2019-10-30
Category : Education
ISBN : 9781470452803

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Random Matrices by Alexei Borodin,Ivan Corwin,Alice Guionnet Pdf

Random matrix theory has many roots and many branches in mathematics, statistics, physics, computer science, data science, numerical analysis, biology, ecology, engineering, and operations research. This book provides a snippet of this vast domain of study, with a particular focus on the notations of universality and integrability. Universality shows that many systems behave the same way in their large scale limit, while integrability provides a route to describe the nature of those universal limits. Many of the ten contributed chapters address these themes, while others touch on applications of tools and results from random matrix theory. This book is appropriate for graduate students and researchers interested in learning techniques and results in random matrix theory from different perspectives and viewpoints. It also captures a moment in the evolution of the theory, when the previous decade brought major break-throughs, prompting exciting new directions of research.

Modern Aspects of Random Matrix Theory

Van H. Vu
Modern Aspects of Random Matrix Theory Book PDF

Author : Van H. Vu
Publisher : American Mathematical Society
Page : 186 pages
File Size : 49,9 Mb
Release : 2014-07-16
Category : Mathematics
ISBN : 9780821894712

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Modern Aspects of Random Matrix Theory by Van H. Vu Pdf

The theory of random matrices is an amazingly rich topic in mathematics. Random matrices play a fundamental role in various areas such as statistics, mathematical physics, combinatorics, theoretical computer science, number theory and numerical analysis. This volume is based on lectures delivered at the 2013 AMS Short Course on Random Matrices, held January 6-7, 2013 in San Diego, California. Included are surveys by leading researchers in the field, written in introductory style, aiming to provide the reader a quick and intuitive overview of this fascinating and rapidly developing topic. These surveys contain many major recent developments, such as progress on universality conjectures, connections between random matrices and free probability, numerical algebra, combinatorics and high-dimensional geometry, together with several novel methods and a variety of open questions.

A Mathematical Introduction to Compressive Sensing

Simon Foucart,Holger Rauhut
A Mathematical Introduction to Compressive Sensing Book PDF

Author : Simon Foucart,Holger Rauhut
Publisher : Springer Science & Business Media
Page : 634 pages
File Size : 41,9 Mb
Release : 2013-08-13
Category : Computers
ISBN : 9780817649487

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A Mathematical Introduction to Compressive Sensing by Simon Foucart,Holger Rauhut Pdf

At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians. A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing.

Compressive Sensing for Urban Radar

Moeness Amin
Compressive Sensing for Urban Radar Book PDF

Author : Moeness Amin
Publisher : CRC Press
Page : 508 pages
File Size : 55,5 Mb
Release : 2017-12-19
Category : Technology & Engineering
ISBN : 9781466597853

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Compressive Sensing for Urban Radar by Moeness Amin Pdf

With the emergence of compressive sensing and sparse signal reconstruction, approaches to urban radar have shifted toward relaxed constraints on signal sampling schemes in time and space, and to effectively address logistic difficulties in data acquisition. Traditionally, these challenges have hindered high resolution imaging by restricting both bandwidth and aperture, and by imposing uniformity and bounds on sampling rates. Compressive Sensing for Urban Radar is the first book to focus on a hybrid of two key areas: compressive sensing and urban sensing. It explains how reliable imaging, tracking, and localization of indoor targets can be achieved using compressed observations that amount to a tiny percentage of the entire data volume. Capturing the latest and most important advances in the field, this state-of-the-art text: Covers both ground-based and airborne synthetic aperture radar (SAR) and uses different signal waveforms Demonstrates successful applications of compressive sensing for target detection and revealing building interiors Describes problems facing urban radar and highlights sparse reconstruction techniques applicable to urban environments Deals with both stationary and moving indoor targets in the presence of wall clutter and multipath exploitation Provides numerous supporting examples using real data and computational electromagnetic modeling Featuring 13 chapters written by leading researchers and experts, Compressive Sensing for Urban Radar is a useful and authoritative reference for radar engineers and defense contractors, as well as a seminal work for graduate students and academia.

Compressive Sensing of Earth Observations

C.H. Chen
Compressive Sensing of Earth Observations Book PDF

Author : C.H. Chen
Publisher : CRC Press
Page : 379 pages
File Size : 45,8 Mb
Release : 2017-05-25
Category : Technology & Engineering
ISBN : 9781498774383

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Compressive Sensing of Earth Observations by C.H. Chen Pdf

Future remote sensing systems will make extensive use of Compressive Sensing (CS) as it becomes more integrated into the system design with increased high resolution sensor developments and the rising earth observation data generated each year. Written by leading experts in the field Compressive Sensing of Earth Observations provides a comprehensive and balanced coverage of the theory and applications of CS in all aspects of earth observations. This work covers a myriad of practical aspects such as the use of CS in detection of human vital signs in a cluttered environment and the corresponding modeling of rib-cage breathing. Readers are also presented with three different applications of CS to the ISAR imaging problem, which includes image reconstruction from compressed data, resolution enhancement, and image reconstruction from incomplete data.

Theoretical Foundations and Numerical Methods for Sparse Recovery

Massimo Fornasier
Theoretical Foundations and Numerical Methods for Sparse Recovery Book PDF

Author : Massimo Fornasier
Publisher : Walter de Gruyter
Page : 351 pages
File Size : 53,5 Mb
Release : 2010-07-30
Category : Mathematics
ISBN : 9783110226157

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Theoretical Foundations and Numerical Methods for Sparse Recovery by Massimo Fornasier Pdf

The present collection is the very first contribution of this type in the field of sparse recovery. Compressed sensing is one of the important facets of the broader concept presented in the book, which by now has made connections with other branches such as mathematical imaging, inverse problems, numerical analysis and simulation. The book consists of four lecture notes of courses given at the Summer School on "Theoretical Foundations and Numerical Methods for Sparse Recovery" held at the Johann Radon Institute for Computational and Applied Mathematics in Linz, Austria, in September 2009. This unique collection will be of value for a broad community and may serve as a textbook for graduate courses. From the contents: "Compressive Sensing and Structured Random Matrices" by Holger Rauhut "Numerical Methods for Sparse Recovery" by Massimo Fornasier "Sparse Recovery in Inverse Problems" by Ronny Ramlau and Gerd Teschke "An Introduction to Total Variation for Image Analysis" by Antonin Chambolle, Vicent Caselles, Daniel Cremers, Matteo Novaga and Thomas Pock