LEADER 04982oam 2200553 450 001 9910807350903321 005 20190911112729.0 010 $a981-4579-06-8 035 $a(OCoLC)873140220 035 $a(MiFhGG)GVRL8RIX 035 $a(EXLCZ)993710000000092949 100 $a20140709h20142014 uy 0 101 0 $aeng 135 $aurun|---uuuua 181 $ctxt 182 $cc 183 $acr 200 10$aSpectral theory of large dimensional random matrices and its applications to wireless communications and finance statistics $erandom matrix theory and its applications /$fZhidong Bai, Northeast Normal University, China & National University of Singapore, Singapore, Zhaoben Fang, University of Science and Technology of China, China, Ying-Chang Liang, The Singapore Infocomm Research Institute, Singapore 210 1$aSingapore :$cWorld Scientific :$cUniversity of Science and Technology of China Press,$d[2014] 210 4$d?2014 215 $a1 online resource (xi, 220 pages) $cillustrations (some color) 225 0 $aGale eBooks 300 $aThis work is originally published by University of Science and Technology of China Press in 2010. 311 $a981-4579-05-X 320 $aIncludes bibliographical references and index. 327 $aPreface; Contents; 1 Introduction; 1.1 History of RMT and Current Development; 1.1.1 A brief review of RMT; 1.1.2 Spectral Analysis of Large Dimensional Random Matrices; 1.1.3 Limits of Extreme Eigenvalues; 1.1.4 Convergence Rate of ESD; 1.1.5 Circular Law; 1.1.6 CLT of Linear Spectral Statistics; 1.1.7 Limiting Distributions of Extreme Eigenvalues and Spacings; 1.2 Applications to Wireless Communications; 1.3 Applications to Finance Statistics; 2 Limiting Spectral Distributions; 2.1 Semicircular Law; 2.1.1 The iid Case; 2.1.2 Independent but not Identically Distributed 327 $a2.2 Marcenko-Pastur Law2.2.1 MP Law for iid Case; 2.2.2 Generalization to the Non-iid Case; 2.2.3 Proof of Theorem 2.11 by Stieltjes Transform; 2.3 LSD of Products; 2.3.1 Existence of the ESD of SnTn; 2.3.2 Truncation of the ESD of Tn; 2.3.3 Truncation, Centralization and Rescaling of the X-variables; 2.3.4 Sketch of the Proof of Theorem 2.12; 2.3.5 LSD of F Matrix; 2.3.6 Sketch of the Proof of Theorem 2.14; 2.3.7 When T is a Wigner Matrix; 2.4 Hadamard Product; 2.4.1 Truncation and Centralization; 2.4.2 Outlines of Proof of the theorem; 2.5 Circular Law 327 $a2.5.1 Failure of Techniques Dealing with Hermitian Matrices2.5.2 Revisit of Stieltjes Transformation; 2.5.3 A Partial Answer to the Circular Law; 2.5.4 Comments and Extensions of Theorem 2.33; 3 Extreme Eigenvalues; 3.1 Wigner Matrix; 3.2 Sample Covariance Matrix; 3.2.1 Spectral Radius; 3.3 Spectrum Separation; 3.4 Tracy-Widom Law; 3.4.1 TW Law for Wigner Matrix; 3.4.2 TW Law for Sample Covariance Matrix; 4 Central Limit Theorems of Linear Spectral Statistics; 4.1 Motivation and Strategy; 4.2 CLT of LSS for Wigner Matrix; 4.2.1 Outlines of the Proof 327 $a6.2.3 Random Matrix Channels6.2.4 Linearly Precoded Systems; 6.3 Channel Capacity for MIMO Antenna Systems; 6.3.1 Single-Input Single-Output Channels; 6.3.2 MIMO Fading Channels; 6.4 Limiting Capacity of Random MIMO Channels; 6.4.1 CSI-Unknown Case; 6.4.2 CSI-Known Case; 6.5 Concluding Remarks; 7 Limiting Performances of Linear and Iterative Receivers; 7.1 Introduction; 7.2 Linear Equalizers; 7.2.1 ZF Equalizer; 7.2.2 Matched Filter (MF) Equalizer; 7.2.3 MMSE Equalizer; 7.2.4 Suboptimal MMSE Equalizer; 7.3 Limiting SINR Analysis for Linear Receivers; 7.3.1 Random Matrix Channels 327 $a7.3.2 Linearly Precoded Systems 330 $aThe 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 ra 606 $aRandom matrices 606 $aSpectral theory (Mathematics) 606 $aWireless communication systems 606 $aFinance$xStatistics 615 0$aRandom matrices. 615 0$aSpectral theory (Mathematics) 615 0$aWireless communication systems. 615 0$aFinance$xStatistics. 676 $a519.2 700 $aBai$b Zhidong$0614432 702 $aFang$b Zhaoben 702 $aLiang$b Ying-Chang 801 0$bMiFhGG 801 1$bMiFhGG 906 $aBOOK 912 $a9910807350903321 996 $aSpectral theory of large dimensional random matrices and its applications to wireless communications and finance statistics$94090172 997 $aUNINA