Random Matrices
eBook - ePub

Random Matrices

  1. 706 pages
  2. English
  3. ePUB (mobile friendly)
  4. Available on iOS & Android
eBook - ePub

Random Matrices

About this book

Random Matrices 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, traffic and communications networks or stock movement in the financial markets. This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time. - Presentation of many new results in one place for the first time - First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals - Fredholm determinants and Painlevé equations - The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities - Fredholm determinants and inverse scattering theory - Probability densities of random determinants

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Yes, you can access Random Matrices by Madan Lal Mehta in PDF and/or ePUB format, as well as other popular books in Matematica & Algebra lineare. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Academic Press
Year
2004
eBook ISBN
9780080474113
Edition
3
Topic
Matematica
Subtopic
Algebra lineare

Table of contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Inside Front Cover
  5. Copyright page
  6. Preface to the Third Edition
  7. Preface to The Second Edition
  8. Preface to The First Edition
  9. Chapter 1: Introduction
  10. Chapter 2: Gaussian Ensembles. The Joint Probability Density Function for the Matrix Elements
  11. Chapter 3: Gaussian Ensembles. The Joint Probability Density Function for the Eigenvalues
  12. Chapter 4: Gaussian Ensembles. Level Density
  13. Chapter 5: Orthogonal, Skew-Orthogonal and Bi-Orthogonal Polynomials
  14. Chapter 6: Gaussian Unitary Ensemble
  15. Chapter 7: Gaussian Orthogonal Ensemble
  16. Chapter 8: Gaussian Symplectic Ensemble
  17. Chapter 9: Gaussian Ensembles: Brownian Motion Model
  18. Chapter 10: Circular Ensembles
  19. Chapter 11: Circular Ensembles (Continued)
  20. Chapter 12: Circular Ensembles. Thermodynamics
  21. Chapter 13: Gaussian Ensemble of Anti-Symmetric Hermitian Matrices
  22. Chapter 14: A Gaussian Ensemble of Hermitian Matrices with Unequal Real and Imaginary Parts
  23. Chapter 15: Matrices with Gaussian Element Densities But with No Unitary or Hermitian Conditions Imposed
  24. Chapter 16: Statistical Analysis of A Level-Sequence
  25. Chapter 17: Selberg’s Integral and Its Consequences
  26. Chapter 18: Asymptotic Behaviour of Eβ(0, S) by Inverse Scattering
  27. Chapter 19: Matrix Ensembles and Classical Orthogonal Polynomials
  28. Chapter 20: Level Spacing Functions Eβ(r, s); Inter-Relations and Power Series Expansions
  29. Chapter 21: Fredholm Determinants and Painlevé Equations
  30. Chapter 22: Moments of the Characteristic Polynomial in the Three Ensembles of Random Matrices
  31. Chapter 23: Hermitian Matrices Coupled in a Chain
  32. Chapter 24: Gaussian Ensembles. Edge of the Spectrum
  33. Chapter 25: Random Permutations, Circular Unitary Ensemble (Cue) and Gaussian Unitary Ensemble (Gue)
  34. Chapter 26: Probability Densities of the Determinants; Gaussian Ensembles
  35. Chapter 27: Restricted Trace Ensembles
  36. Appendices
  37. Notes
  38. References
  39. Author Index
  40. Subject Index