Statistical theory and random matrices:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York and Basel
Marcel Dekker
[1983]
|
| Series: | Pure and applied mathematics
74 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | ix, 203 Seiten Illustrationen |
| ISBN: | 0824717791 |
Staff View
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Record in the Search Index
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| adam_text | CONTENTS
PREFACE v
Chapter 1 INTRODUCTION 1
1.1 Complex systems 1
1.2 Statistical Theory of Levels 2
1.3 Comparison with Statistical Mechanics 3
1.4 Examples 4
1.5 Distribution of the Widths 7
1.6 Preview 8
Chapter 2 HIGHLY EXCITED SYSTEMS 9
2.1 One Dimensional Systems 9
2.2 Sequences of Numbers 10
2.3 Quantal Spectra 12
Chapter 3 SYMMETRY PROPERTIES OF
PHYSICAL SYSTEMS 15
3.1 Symmetry Properties 15
3.2 Time Reversal 16
3.3 The Hamiltonian Matrix 18
3.4 Relation to Kramers Degeneracy 19
3.5 Quaternion Structure 20
3.6 The Threefold Way of Invariance 21
vii
viii CONTENTS
Chapter 4 GAUSSIAN AND ORTHOGONAL
ENSEMBLES 23
4.1 The Gaussian Ensemble 23
4.2 The Orthogonal Ensemble 24
4.3 The Semicircle Distribution 25
4.4 The Wishart Ensemble 26
4.5 Invariance and Equal Probability 27
Chapter 5 UNITARY ENSEMBLE 29
5.1 Systems without Time Reversal Symmetry 29
5.2 Level Repulsion in Spectra 31
5.3 Repulsion in Low Energy Spectra 39
Chapter 6 EIGENVALUE EIGENVECTOR DISTRIBUTIONS
OF THE GAUSSIAN ENSEMBLE 43
6.1 The Gaussian Ensemble 43
6.2 The Repulsion of Levels 46
6.3 Wigner s Conjecture 47
6.4 Mean Level Density 49
6.5 Remark 50
6.6 The Spectral Rigidity 50
Chapter 7 DISTRIBUTION OF THE WIDTHS 57
7.1 Widths of Energy Levels 57
7.2 The Porter Thomas Distribution 58
7.3 Strength Fluctuations and Collective Behavior 60
7.4 The Porter Thomas Distribution and
Experimental Data 62
Chapter 8 SYMPLECTIC GROUP AND QUATERNIONS 67
8.1 The Symplectic Group 67
8.2 Quaternions 68
8.3 Matrices and Quaternions 69
8.4 Quaternion Algebra 70
8.5 Symplectic Ensemble 72
Chapter 9 MORE ON THE GAUSSIAN ENSEMBLE 75
9.1 The Gaussian Ensemble 75
9.2 The Distribution Function 76
9.3 The Jacobian of the Transformation 78
9.4 Specification of the Distribution Function 79
9.5 The Unitary Ensemble Case 80
CONTENTS ix
Chapter 10 SUMMARY 83
10.1 Random Matrices and Energy Levels 83
10.2 Role of the Hamiltonian 84
10.3 The Wishart Distribution 85
10.4 Recent Studies 85
10.5 Finite and Infinite Matrices 86
Appendix A MULTIVARIATE DISTRIBUTIONS 87
Al. Distributions 87
A2. Preliminaries 88
A3. Distributions of Some Random Matrices 94
A4. Marginal Distributions of Few Roots 100
A5. Moments of the Elementary Symmetric
Functions 104
A6. Distributions of the Ratios of the Roots 108
A7. Distributions of the Likelihood Ratio Test
Statistics 109
Appendix B APPLICATIONS OF MULTIVARIATE
DISTRIBUTIONS 115
Bl. Preliminaries 115
B2. Testing Hypotheses 116
B3. Discrimination between Multivariate Normal
Population 122
B4. Alternative Procedures 123
Appendix C RANDOM MATRICES: ERGODIC
PROPERTIES 129
Cl. Preliminaries 130
C2. One Point Measures 135
C3. Higher Order Functions 139
C4. Behavior of the Strength Distribution 146
C5. Final Remarks 150
REFERENCES 151
BIBLIOGRAPHY 169
INDEX 179
|
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| discipline | Physik Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV003702012 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T16:04:05Z |
| institution | BVB |
| isbn | 0824717791 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002356481 |
| oclc_num | 8975465 |
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| physical | ix, 203 Seiten Illustrationen |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Marcel Dekker |
| record_format | marc |
| series | Pure and applied mathematics |
| series2 | Pure and applied mathematics |
| spelling | Carmeli, Moshe 1933-2007 (DE-588)128455624 aut Statistical theory and random matrices Moshe Carmeli: Center for Theoretical Physics, Ben Gurion University of the Negev, Beer Sheva, Israel New York and Basel Marcel Dekker [1983] © 1983 ix, 203 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Pure and applied mathematics 74 Energieniveaus gtt Matrices Matrices gtt Niveaux d'énergie - Mécanique quantique - Méthodes statistiques Statistische methoden gtt Energy levels (Quantum mechanics) Statistical methods Random matrices Energieniveau (DE-588)4152225-4 gnd rswk-swf Stochastische Matrix (DE-588)4057624-3 gnd rswk-swf Energieniveau (DE-588)4152225-4 s Stochastische Matrix (DE-588)4057624-3 s DE-604 Pure and applied mathematics 74 (DE-604)BV000001885 74 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002356481&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Carmeli, Moshe 1933-2007 Statistical theory and random matrices Pure and applied mathematics Energieniveaus gtt Matrices Matrices gtt Niveaux d'énergie - Mécanique quantique - Méthodes statistiques Statistische methoden gtt Energy levels (Quantum mechanics) Statistical methods Random matrices Energieniveau (DE-588)4152225-4 gnd Stochastische Matrix (DE-588)4057624-3 gnd |
| subject_GND | (DE-588)4152225-4 (DE-588)4057624-3 |
| title | Statistical theory and random matrices |
| title_auth | Statistical theory and random matrices |
| title_exact_search | Statistical theory and random matrices |
| title_full | Statistical theory and random matrices Moshe Carmeli: Center for Theoretical Physics, Ben Gurion University of the Negev, Beer Sheva, Israel |
| title_fullStr | Statistical theory and random matrices Moshe Carmeli: Center for Theoretical Physics, Ben Gurion University of the Negev, Beer Sheva, Israel |
| title_full_unstemmed | Statistical theory and random matrices Moshe Carmeli: Center for Theoretical Physics, Ben Gurion University of the Negev, Beer Sheva, Israel |
| title_short | Statistical theory and random matrices |
| title_sort | statistical theory and random matrices |
| topic | Energieniveaus gtt Matrices Matrices gtt Niveaux d'énergie - Mécanique quantique - Méthodes statistiques Statistische methoden gtt Energy levels (Quantum mechanics) Statistical methods Random matrices Energieniveau (DE-588)4152225-4 gnd Stochastische Matrix (DE-588)4057624-3 gnd |
| topic_facet | Energieniveaus Matrices Niveaux d'énergie - Mécanique quantique - Méthodes statistiques Statistische methoden Energy levels (Quantum mechanics) Statistical methods Random matrices Energieniveau Stochastische Matrix |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002356481&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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