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Theory of Random Determinants

  • Book
  • © 1990

Overview

Authors:
  1. V. L. Girko

    1. Dapartment of Cybernetics, Kiev State University, USSR

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Part of the book series: Mathematics and its Applications (MASS, volume 45)

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Table of contents (28 chapters)

  1. Front Matter

    Pages i-xxv
    Download chapter PDF

  2. Generalized Wishart Density and Integral Representation for Determinants

    • V. L. Girko
    Pages 1-21

  3. Moments of Random Matrix Determinants

    • V. L. Girko
    Pages 22-53

  4. Distribution of Eigenvalues and Eigenvectors of Random Matrices

    • V. L. Girko
    Pages 54-101

  5. Inequalities for Random Determinants

    • V. L. Girko
    Pages 102-113

  6. Limit Theorems for the Borel Functions of Independent Random Variables

    • V. L. Girko
    Pages 114-169

  7. Limit Theorems of the Law of Large Numbers and Central Limit Theorem Types for Random Determinants

    • V. L. Girko
    Pages 170-203

  8. Accompanying Infinitely Divisible Laws for Random Determinants

    • V. L. Girko
    Pages 204-217

  9. Integral Representation Method

    • V. L. Girko
    Pages 218-254

  10. The Connection Between the Convergence of Random Determinants and the Convergence of Functionals of Random Functions

    • V. L. Girko
    Pages 255-296

  11. Limit Theorems for Random Gram Determinants

    • V. L. Girko
    Pages 297-308

  12. The Determinants of Toeplitz and Hankel Random Matrices

    • V. L. Girko
    Pages 309-320

  13. Limit Theorems for Determinants of Random Jacobi Matrices

    • V. L. Girko
    Pages 321-346

  14. The Fredholm Random Determinants

    • V. L. Girko
    Pages 347-365

  15. The Systems of Linear Algebraic Equations with Random Coefficients

    • V. L. Girko
    Pages 366-376

  16. Limit Theorems for the Solution of the Systems of Linear Algebraic Equations with Random Coefficients

    • V. L. Girko
    Pages 377-390

  17. Integral Equations with Random Degenerate Kernels

    • V. L. Girko
    Pages 391-400

  18. Random Determinants in the Spectral Theory of Non-Self-Adjoint Random Matrices

    • V. L. Girko
    Pages 401-441

  19. The Distribution of Eigenvalues and Eigenvectors of Additive Random Matrix-Valued Processes

    • V. L. Girko
    Pages 442-467

  20. The Stochastic Ljapunov Problem for Systems of Stationary Linear Differential Equations

    • V. L. Girko
    Pages 468-480
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Keywords

Authors and Affiliations

  • Dapartment of Cybernetics, Kiev State University, USSR

    V. L. Girko

About the author

Vyacheslav L. Girko is Professor of Mathematics in the Department of Applied Statistics at the National University of Kiev and the University of Kiev Mohyla Academy. He is also affiliated with the Institute of Mathematics, Ukrainian Academy of Sciences. His research interests include multivariate statistical analysis, discriminant analysis, experiment planning, identification and control of complex systems, statistical methods in physics, noise filtration, matrix analysis, and stochastic optimization. He has published widely in the areas of multidimensional statistical analysis and theory of random matrices.

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