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Random matrices /
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, chaoti...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; San Diego, CA :
Academic Press,
2004.
|
| Edición: | 3rd ed. |
| Colección: | Pure and applied mathematics (Academic Press) ;
142. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo Texto completo Texto completo |
Tabla de Contenidos:
- Cover
- Contents
- Preface to the Third Edition
- Preface to the Second Edition
- Preface to the First Edition
- Introduction
- Random Matrices in Nuclear Physics
- Random Matrices in Other Branches of Knowledge
- A Summary of Statistical Facts about Nuclear Energy Levels
- Level Density
- Distribution of Neutron Widths
- Radiation and Fission Widths
- Level Spacings
- Definition of a Suitable Function for the Study of Level Correlations
- Wigner Surmise
- Electromagnetic Properties of Small Metallic Particles
- Analysis of Experimental Nuclear Levels
- The Zeros of The Riemann Zeta Function
- Things Worth Consideration, But Not Treated in This Book
- Gaussian Ensembles. The Joint Probability Density Function for the Matrix Elements
- Preliminaries
- Time-Reversal Invariance
- Gaussian Orthogonal Ensemble
- Gaussian Symplectic Ensemble
- Gaussian Unitary Ensemble
- Joint Probability Density Function for the Matrix Elements
- Gaussian Ensemble of Hermitian Matrices With Unequal Real and Imaginary Parts
- Anti-Symmetric Hermitian Matrices
- Summary of Chapter 2
- Gaussian Ensembles. The Joint Probability Density Function for the Eigenvalues
- Orthogonal Ensemble
- Symplectic Ensemble
- Unitary Ensemble
- Ensemble of Anti-Symmetric Hermitian Matrices
- Gaussian Ensemble of Hermitian Matrices With Unequal Real and Imaginary Parts
- Random Matrices and Information Theory
- Summary of Chapter 3
- Gaussian Ensembles. Level Density
- The Partition Function
- The Asymptotic Formula for the Level Density. Gaussian Ensembles
- The Asymptotic Formula for the Level Density. Other Ensembles
- Summary of Chapter 4
- Orthogonal, Skew-Orthogonal and Bi-Orthogonal Polynomials
- Quaternions, Pfaffians, Determinants
- Average Value of PI N j=1 f (xj); Orthogonal and Skew-Orthogonal Polynomials
- Case beta = 2; Orthogonal Polynomials
- Case beta = 4; Skew-Orthogonal Polynomials of Quaternion Type
- Case beta = 1; Skew-Orthogonal Polynomials of Real Type
- Average Value of Pi j=1N psi(xj, yj); Bi-Orthogonal Polynomials
- Correlation Functions
- Proof of Theorem 5.7.1
- Case beta = 2
- Case beta = 4
- Case beta = 1, Even Number of Variables
- Case beta = 1, Odd Number of Variables
- Spacing Functions
- Determinantal Representations
- Integral Representations
- Properties of the Zeros
- Orthogonal Polynomials and the Riemann-Hilbert Problem
- A Remark (Balian)
- Summary of Chapter 5
- Gaussian Unitary Ensemble
- Generalities
- About Correlation and Cluster Functions
- About Level-Spacings
- Spacing Distribution
- Correlations and Spacings
- The n-Point Correlation Function
- Level Spacings
- Several Consecutive Spacings
- Some Remarks
- Summary of Chapter 6
- Gaussian Orthogonal Ensemble
- Generalities
- Correlation and Cluster Functions
- Level Spacings. Integration Over Alternate Variables
- Several Consecutive Spacings: n = 2r
- Several Consecutive Spacings: n = 2r
- 1
- Case n = 1
- Case n = 2r
- 1
- Bounds for the Distribution Function of the Spacings
- Summary of Chapter 7
- Gaussian Symplectic Ensem.