Random matrix theory and its applications :: multivariate statistics and wireless communications /
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...
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| Weitere Verfasser: | , , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ :
World Scientific,
©2009.
|
| Schriftenreihe: | Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ;
v. 18. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | 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, th. |
| Beschreibung: | 1 online resource (x, 165 pages) : illustrations |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9789814273121 9814273120 1282758047 9781282758049 9786612758041 661275804X |
| ISSN: | 1793-0758 ; |
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| 245 | 0 | 0 | |a Random matrix theory and its applications : |b multivariate statistics and wireless communications / |c editors, Zhidong Bai, Yang Chen, Ying-Chang Liang. |
| 260 | |a Hackensack, NJ : |b World Scientific, |c ©2009. | ||
| 300 | |a 1 online resource (x, 165 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Lecture notes series, |x 1793-0758 ; |v v. 18 | |
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a 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, th. | ||
| 505 | 0 | |6 880-01 |a 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. | |
| 505 | 8 | |a 2. Physical Random Matrix Ensembles2.1. 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. | |
| 505 | 8 | |a Future of Statistics Zhidong Bai and Shurong Zheng1. 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. | |
| 505 | 8 | |a 8. Example: Analysis of Large CDMA Systems8.1. Gaussian prior distribution; 8.2. Binary prior distribution; 8.3. Arbitrary prior distribution; 9. Phase Transitions; References. | |
| 546 | |a English. | ||
| 650 | 0 | |a Random matrices. |0 http://id.loc.gov/authorities/subjects/sh86001920 | |
| 650 | 4 | |a Algebra. | |
| 650 | 4 | |a Physical Sciences & Mathematics. | |
| 650 | 4 | |a Random matrices. | |
| 650 | 4 | |a Mathematics. | |
| 650 | 6 | |a Matrices aléatoires. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a Random matrices |2 fast | |
| 700 | 1 | |a Bai, Zhidong. | |
| 700 | 1 | |a Chen, Yang. | |
| 700 | 1 | |a Liang, Ying-Chang. | |
| 758 | |i has work: |a Random matrix theory and its applications (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGfTdVMM3rjqTQvJfKwQv3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |t Random matrix theory and its applications. |d Hackensack, NJ : World Scientific, ©2009 |z 9789814273114 |w (OCoLC)298782419 |
| 830 | 0 | |a Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ; |v v. 18. |0 http://id.loc.gov/authorities/names/no2003042729 | |
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| 880 | 8 | |6 505-01/(S |a 3. Why Asymptotic Random Matrix Theory4. η 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.M uller; 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. | |
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| contents | 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. 2. Physical Random Matrix Ensembles2.1. 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. Future of Statistics Zhidong Bai and Shurong Zheng1. 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. 8. Example: Analysis of Large CDMA Systems8.1. Gaussian prior distribution; 8.2. Binary prior distribution; 8.3. Arbitrary prior distribution; 9. Phase Transitions; References. |
| ctrlnum | (OCoLC)671648582 |
| dewey-full | 512 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| id | ZDB-4-EBA-ocn671648582 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:17:34Z |
| institution | BVB |
| isbn | 9789814273121 9814273120 1282758047 9781282758049 9786612758041 661275804X |
| issn | 1793-0758 ; |
| language | English |
| lccn | 2009282238 |
| oclc_num | 671648582 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (x, 165 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | World Scientific, |
| record_format | marc |
| series | Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ; |
| series2 | Lecture notes series, |
| spelling | Random matrix theory and its applications : multivariate statistics and wireless communications / editors, Zhidong Bai, Yang Chen, Ying-Chang Liang. Hackensack, NJ : World Scientific, ©2009. 1 online resource (x, 165 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Lecture notes series, 1793-0758 ; v. 18 Includes bibliographical references. Print version record. 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, th. 880-01 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. 2. Physical Random Matrix Ensembles2.1. 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. Future of Statistics Zhidong Bai and Shurong Zheng1. 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. 8. Example: Analysis of Large CDMA Systems8.1. Gaussian prior distribution; 8.2. Binary prior distribution; 8.3. Arbitrary prior distribution; 9. Phase Transitions; References. English. Random matrices. http://id.loc.gov/authorities/subjects/sh86001920 Algebra. Physical Sciences & Mathematics. Random matrices. Mathematics. Matrices aléatoires. MATHEMATICS Algebra Intermediate. bisacsh Random matrices fast Bai, Zhidong. Chen, Yang. Liang, Ying-Chang. has work: Random matrix theory and its applications (Text) https://id.oclc.org/worldcat/entity/E39PCGfTdVMM3rjqTQvJfKwQv3 https://id.oclc.org/worldcat/ontology/hasWork Print version: Random matrix theory and its applications. Hackensack, NJ : World Scientific, ©2009 9789814273114 (OCoLC)298782419 Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ; v. 18. http://id.loc.gov/authorities/names/no2003042729 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340508 Volltext 505-01/(S 3. Why Asymptotic Random Matrix Theory4. η 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.M uller; 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. |
| spellingShingle | Random matrix theory and its applications : multivariate statistics and wireless communications / Lecture notes series (National University of Singapore. Institute for Mathematical Sciences) ; 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. 2. Physical Random Matrix Ensembles2.1. 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. Future of Statistics Zhidong Bai and Shurong Zheng1. 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. 8. Example: Analysis of Large CDMA Systems8.1. Gaussian prior distribution; 8.2. Binary prior distribution; 8.3. Arbitrary prior distribution; 9. Phase Transitions; References. Random matrices. http://id.loc.gov/authorities/subjects/sh86001920 Algebra. Physical Sciences & Mathematics. Random matrices. Mathematics. Matrices aléatoires. MATHEMATICS Algebra Intermediate. bisacsh Random matrices fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh86001920 |
| title | Random matrix theory and its applications : multivariate statistics and wireless communications / |
| title_auth | Random matrix theory and its applications : multivariate statistics and wireless communications / |
| title_exact_search | Random matrix theory and its applications : multivariate statistics and wireless communications / |
| title_full | Random matrix theory and its applications : multivariate statistics and wireless communications / editors, Zhidong Bai, Yang Chen, Ying-Chang Liang. |
| title_fullStr | Random matrix theory and its applications : multivariate statistics and wireless communications / editors, Zhidong Bai, Yang Chen, Ying-Chang Liang. |
| title_full_unstemmed | Random matrix theory and its applications : multivariate statistics and wireless communications / editors, Zhidong Bai, Yang Chen, Ying-Chang Liang. |
| title_short | Random matrix theory and its applications : |
| title_sort | random matrix theory and its applications multivariate statistics and wireless communications |
| title_sub | multivariate statistics and wireless communications / |
| topic | Random matrices. http://id.loc.gov/authorities/subjects/sh86001920 Algebra. Physical Sciences & Mathematics. Random matrices. Mathematics. Matrices aléatoires. MATHEMATICS Algebra Intermediate. bisacsh Random matrices fast |
| topic_facet | Random matrices. Algebra. Physical Sciences & Mathematics. Mathematics. Matrices aléatoires. MATHEMATICS Algebra Intermediate. Random matrices |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=340508 |
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