LEADER 05179nam 2200661 a 450 001 9910455882803321 005 20210729011024.0 010 $a1-282-75804-7 010 $a9786612758041 010 $a981-4273-12-0 035 $a(CKB)2490000000001606 035 $a(EBL)1679389 035 $a(OCoLC)671648582 035 $a(SSID)ssj0000426666 035 $a(PQKBManifestationID)12104272 035 $a(PQKBTitleCode)TC0000426666 035 $a(PQKBWorkID)10390105 035 $a(PQKB)11523735 035 $a(MiAaPQ)EBC1679389 035 $a(WSP)00007285 035 $a(Au-PeEL)EBL1679389 035 $a(CaPaEBR)ebr10422343 035 $a(CaONFJC)MIL275804 035 $a(EXLCZ)992490000000001606 100 $a20091211d2009 uy 0 101 0 $aeng 135 $aurcn||||||||| 181 $ctxt 182 $cc 183 $acr 200 00$aRandom matrix theory and its applications$b[electronic resource] $emultivariate statistics and wireless communications /$feditors, Zhidong Bai, Yang Chen, Ying-Chang Liang 210 $aHackensack, N.J. $cWorld Scientific$dc2009 215 $a1 online resource (176 p.) 225 1 $aLecture notes series, Institute for Mathematical Sciences, National University of Singapore,$x1793-0758 ;$vv. 18 300 $aDescription based upon print version of record. 311 $a981-4273-11-2 320 $aIncludes bibliographical references. 327 $aCONTENTS; Foreword; Preface; The Stieltjes Transform and its Role in Eigenvalue Behavior of Large Dimensional Random Matrices Jack W. Silverstein; 1. Introduction; 2. Why These Theorems are True; 3. The Other Equations; 4. Proof of Uniqueness of (1.1); 5. Truncation and Centralization; 6. The Limiting Distributions; 7. Other Uses of the Stieltjes Transform; References; Beta Random Matrix Ensembles Peter J. Forrester; 1. Introduction; 1.1. Log-gas systems; 1.2. Quantum many body systems; 1.3. Selberg correlation integrals; 1.4. Correlation functions; 1.5. Scaled limits 327 $a2. Physical Random Matrix Ensembles 2.1. Heavy nuclei and quantum mechanics; 2.2. Dirac operators and QCD; 2.3. Random scattering matrices; 2.4. Quantum conductance problems; 2.5. Eigenvalue p.d.f.'s for Hermitian matrices; 2.6. Eigenvalue p.d.f.'s for Wishart matrices; 2.7. Eigenvalue p.d.f.'s for unitary matrices; 2.8. Eigenvalue p.d.f.'s for blocks of unitary matrices; 2.9. Classical random matrix ensembles; 3. -Ensembles of Random Matrices; 3.1. Gaussian ensemble; 4. Laguerre Ensemble; 5. Recent Developments; Acknowledgments; References 327 $aFuture of Statistics Zhidong Bai and Shurong Zheng 1. Introduction; 2. A Multivariate Two-Sample Problem; 2.1. Asymptotic power of T 2 test; 2.2. Dempster's NET; 2.3. Bai and Saranadasa's ANT; 2.4. Conclusions and simulations; 3. A Likelihood Ratio Test on Covariance Matrix; 3.1. Classical tests; 3.2. Random matrix theory; 3.3. Testing based on RMT limiting CLT; 3.4. Simulation results; 4. Conclusions; Acknowledgment; References; The and Shannon Transforms: A Bridge between Random Matrices and Wireless Communications Antonia M. Tulino; 1. Introduction; 2. Wireless Communication Channels 327 $a3. Why Asymptotic Random Matrix Theory? 4. ? and Shannon Transforms: Theory and Applications; 5. Applications to Wireless Communications; 5.1. CDMA; 5.1.1. DS-CDMA frequency-flat fading; 5.1.2. Multi-carrier CDMA; 5.2. Multi-antenna channels; 5.3. Separable correlation model; 5.4. Non-separable correlation model; 5.5. Non-ergodic channels; References; The Replica Method in Multiuser Communications Ralf R. Muller; 1. Introduction; 2. Self Average; 3. Free Energy; 4. The Meaning of the Energy Function; 5. Replica Continuity; 6. Saddle Point Integration; 7. Replica Symmetry 327 $a8. Example: Analysis of Large CDMA Systems 8.1. Gaussian prior distribution; 8.2. Binary prior distribution; 8.3. Arbitrary prior distribution; 9. Phase Transitions; References 330 $aRandom matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of the energy levels of heavy nuclei. The subject was further deeply developed under the important leadership of Dyson, Gaudin and Mehta, and other mathematical physicists. In the early 1990's, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, 410 0$aLecture notes series (National University of Singapore. Institute for Mathematical Sciences) ;$vv. 18. 606 $aRandom matrices 608 $aElectronic books. 615 0$aRandom matrices. 676 $a512.9434 701 $aBai$b Zhidong$0614432 701 $aChen$b Yang$c(Mathematics teacher)$0971908 701 $aLiang$b Ying-Chang$0899604 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910455882803321 996 $aRandom matrix theory and its applications$92209772 997 $aUNINA