UID:
almahu_9947366296702882
Format:
1 online resource (707 p.)
Edition:
3rd ed.
ISBN:
1-280-96818-4
,
9786610968183
,
0-08-047411-X
Series Statement:
Pure and applied mathematics (Academic Press), 142
Content:
This book gives a coherent and detailed description of analytical methods devised to study random matrices. These methods are critical to the understanding of various fields in in mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other zeta functions. More generally they apply to the characteristic energies of any sufficiently complicated system and which have found, since the publication of the second edition, many new applications in active research areas such as quantum gravity, tra
Note:
Description based upon print version of record.
,
Front Cover; Random Matrices; Copyright Page; Contents; Preface to the Third Edition; Preface to the Second Edition; Preface to the First Edition; Chapter 1. Introduction; 1.1. Random Matrices in Nuclear Physics; 1.2. Random Matrices in Other Branches of Knowledge; 1.3. A Summary of Statistical Facts about Nuclear Energy Levels; 1.4. Definition of a Suitable Function for the Study of Level Correlations; 1.5. Wigner Surmise; 1.6. Electromagnetic Properties of Small Metallic Particles; 1.7. Analysis of Experimental Nuclear Levels; 1.8. The Zeros of the Riemann Zeta Function
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1.9. Things Worth Consideration, But Not Treated in This BookChapter 2. Gaussian Ensembles. The Joint Probability Density Function for the Matrix Elements; 2.1. Preliminaries; 2.2. Time-Reversal Invariance; 2.3. Gaussian Orthogonal Ensemble; 2.4. Gaussian Symplectic Ensemble; 2.5. Gaussian Unitary Ensemble; 2.6. Joint Probability Density Function for the Matrix Elements; 2.7. Gaussian Ensemble of Hermitian Matrices With Unequal Real and Imaginary Parts; 2.8. Anti-Symmetric Hermitian Matrices; Summary of Chapter 2
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Chapter 3. Gaussian Ensembles. The Joint Probability Density Function for the Eigenvalues3.1. Orthogonal Ensemble; 3.2. Symplectic Ensemble; 3.3. Unitary Ensemble; 3.4. Ensemble of Anti-Symmetric Hermitian Matrices; 3.5. Gaussian Ensemble of Hermitian Matrices With Unequal Real and Imaginary Parts; 3.6. Random Matrices and Information Theory; Summary of Chapter 3; Chapter 4. Gaussian Ensembles Level Density; 4.1. The Partition Function; 4.2. The Asymptotic Formula for the Level Density. Gaussian Ensembles; 4.3. The Asymptotic Formula for the Level Density. Other Ensembles
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5.11. Integral Representations5.12. Properties of the Zeros; 5.13. Orthogonal Polynomials and the Riemann-Hilbert Problem; 5.14. A Remark (Balian); Summary of Chapter 5; Chapter 6. Gaussian Unitary Ensemble; 6.1. Generalities; 6.2. The n-Point Correlation Function; 6.3. Level Spacings; 6.4. Several Consecutive Spacings; 6.5. Some Remarks; Summary of Chapter 6; Chapter 7. Gaussian Orthogonal Ensemble; 7.1. Generalities; 7.2. Correlation and Cluster Functions; 7.3. Level Spacings. Integration Over Alternate Variables; 7.4. Several Consecutive Spacings: n = 2r
,
7.5. Several Consecutive Spacings: n = 2r - 1
,
English
Additional Edition:
ISBN 1-4832-9989-9
Additional Edition:
ISBN 0-12-088409-7
Language:
English
