Random Matrices: High Dimensional Phenomena
eBook - PDF

Random Matrices: High Dimensional Phenomena

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Random Matrices: High Dimensional Phenomena

About this book

This book focuses on the behaviour of large random matrices. Standard results are covered, and the presentation emphasizes elementary operator theory and differential equations, so as to be accessible to graduate students and other non-experts. The introductory chapters review material on Lie groups and probability measures in a style suitable for applications in random matrix theory. Later chapters use modern convexity theory to establish subtle results about the convergence of eigenvalue distributions as the size of the matrices increases. Random matrices are viewed as geometrical objects with large dimension. The book analyzes the concentration of measure phenomenon, which describes how measures behave on geometrical objects with large dimension. To prove such results for random matrices, the book develops the modern theory of optimal transportation and proves the associated functional inequalities involving entropy and information. These include the logarithmic Sobolev inequality, which measures how fast some physical systems converge to equilibrium.

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Yes, you can access Random Matrices: High Dimensional Phenomena by Gordon Blower in PDF and/or ePUB format, as well as other popular books in Mathematics & Probability & Statistics. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. Contents
  6. Introduction
  7. 1 Metric measure spaces
  8. 2 Lie groups and matrix ensembles
  9. 3 Entropy and concentration of measure
  10. 4 Free entropy and equilibrium
  11. 5 Convergence to equilibrium
  12. 6 Gradient flows and functional inequalities
  13. 7 Young tableaux
  14. 8 Random point fields and random matrices
  15. 9 Integrable operators and differential equations
  16. 10 Fluctuations and the Tracy-Widom distribution
  17. 11 Limit groups and Gaussian measures
  18. 12 Hermite polynomials
  19. 13 From the Ornstein-Uhlenbeck process to the Burgers equation
  20. 14 Noncommutative probability spaces
  21. References
  22. Index