Theory of Random Determinants / Edition 1

by V.L. Girko

Overview

'Et mm. ..., si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point all': '' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf IIClI.t to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.

Product Details

ISBN-13:	9780792302339
Publisher:	Springer Netherlands
Publication date:	09/30/1990
Series:	Mathematics and its Applications , #45
Edition description:	1990
Pages:	678
Product dimensions:	6.14(w) x 9.21(h) x 0.36(d)

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 shastic optimization. He has published widely in the areas of multidimensional statistical analysis and theory of random matrices.

Table of Contents

1. Generalized Wishart Density and Integral Representation for Determinants.- 2. Moments of Random Matrix Determinants.- 3. Distribution of Eigenvalues and Eigenvectors of Random Matrices.- 4. Inequalities for Random Determinants.- 5. Limit Theorems for the Borel Functions of Independent Random Variables.- 6. Limit Theorems of the Law of Large Numbers and Central Limit Theorem Types for Random Determinants.- 7. Accompanying Infinitely Divisible Laws for Random Determinants.- 8. Integral Representation Method.- 9. The Connection between the Convergence of Random Determinants and the Convergence of Functionals of Random Functions.- 10. Limit Theorems for Random Gram Determinants.- 11. The Determinants of Toeplitz and Hankel Random Matrices.- 12. Limit Theorems for Determinants of Random Jacobi Matrices.- 13. The Fredholm Random Determinants.- 14. The Systems of Linear Algebraic Equations with Random Coefficients.- 15. Limit Theorems for the Solution of the Systems of Linear Algebraic Equations with Random Coefficients.- 16. Integral Equations with Random Degenerate Kernels.- 17. Random Determinants in the Spectral Theory of Non-Self-Adjoint Random Matrices.- 18. The Distribution of Eigenvalues and Eigenvectors of Additive Random Matrix-Valued Processes.- 19. The Shastic Ljapunov Problem for Systems of Stationary Linear Differential Equations.- 20. Random Determinants in the Theory of Estimation of Parameters of Some Systems.- 21. Random Determinants in Some Problems of Control Theory of Shastic Systems.- 22. Random Determinants in Some Linear Shastic Programming Problems.- 23. Random Determinants in General Statistical Analysis.- 24. Estimate of the Solution of the Kolmogorov-Wiener Filter.- 25. Random Determinants in Pattern Recognition.- 26. Random Determinantsin the Experiment Design.- 27. Random Determinants in Physics.- 28. Random Determinants in Numerical Analysis.- References.