Ebook: Theory of Random Determinants

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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Content:
Front Matter....Pages i-xxv
Generalized Wishart Density and Integral Representation for Determinants....Pages 1-21
Moments of Random Matrix Determinants....Pages 22-53
Distribution of Eigenvalues and Eigenvectors of Random Matrices....Pages 54-101
Inequalities for Random Determinants....Pages 102-113
Limit Theorems for the Borel Functions of Independent Random Variables....Pages 114-169
Limit Theorems of the Law of Large Numbers and Central Limit Theorem Types for Random Determinants....Pages 170-203
Accompanying Infinitely Divisible Laws for Random Determinants....Pages 204-217
Integral Representation Method....Pages 218-254
The Connection Between the Convergence of Random Determinants and the Convergence of Functionals of Random Functions....Pages 255-296
Limit Theorems for Random Gram Determinants....Pages 297-308
The Determinants of Toeplitz and Hankel Random Matrices....Pages 309-320
Limit Theorems for Determinants of Random Jacobi Matrices....Pages 321-346
The Fredholm Random Determinants....Pages 347-365
The Systems of Linear Algebraic Equations with Random Coefficients....Pages 366-376
Limit Theorems for the Solution of the Systems of Linear Algebraic Equations with Random Coefficients....Pages 377-390
Integral Equations with Random Degenerate Kernels....Pages 391-400
Random Determinants in the Spectral Theory of Non-Self-Adjoint Random Matrices....Pages 401-441
The Distribution of Eigenvalues and Eigenvectors of Additive Random Matrix-Valued Processes....Pages 442-467
The Stochastic Ljapunov Problem for Systems of Stationary Linear Differential Equations....Pages 468-480
Random Determinants in the Theory of Estimation of Parameters of Some Systems....Pages 481-502
Random Determinants in Some Problems of Control Theory of Stochastic Systems....Pages 503-526
Random Determinants in Some Linear Stochastic Programming Problems....Pages 527-538
Random Determinants in General Statistical Analysis....Pages 539-587
Estimate of the Solution of the Kolmogorov-Wiener Filter....Pages 588-594
Random Determinants in Pattern Recognition....Pages 595-615
Random Determinants in the Experiment Design....Pages 616-626
Random Determinants in Physics....Pages 627-643
Random Determinants in Numerical Analysis....Pages 644-656
Back Matter....Pages 657-677

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Content:
Front Matter....Pages i-xxv
Generalized Wishart Density and Integral Representation for Determinants....Pages 1-21
Moments of Random Matrix Determinants....Pages 22-53
Distribution of Eigenvalues and Eigenvectors of Random Matrices....Pages 54-101
Inequalities for Random Determinants....Pages 102-113
Limit Theorems for the Borel Functions of Independent Random Variables....Pages 114-169
Limit Theorems of the Law of Large Numbers and Central Limit Theorem Types for Random Determinants....Pages 170-203
Accompanying Infinitely Divisible Laws for Random Determinants....Pages 204-217
Integral Representation Method....Pages 218-254
The Connection Between the Convergence of Random Determinants and the Convergence of Functionals of Random Functions....Pages 255-296
Limit Theorems for Random Gram Determinants....Pages 297-308
The Determinants of Toeplitz and Hankel Random Matrices....Pages 309-320
Limit Theorems for Determinants of Random Jacobi Matrices....Pages 321-346
The Fredholm Random Determinants....Pages 347-365
The Systems of Linear Algebraic Equations with Random Coefficients....Pages 366-376
Limit Theorems for the Solution of the Systems of Linear Algebraic Equations with Random Coefficients....Pages 377-390
Integral Equations with Random Degenerate Kernels....Pages 391-400
Random Determinants in the Spectral Theory of Non-Self-Adjoint Random Matrices....Pages 401-441
The Distribution of Eigenvalues and Eigenvectors of Additive Random Matrix-Valued Processes....Pages 442-467
The Stochastic Ljapunov Problem for Systems of Stationary Linear Differential Equations....Pages 468-480
Random Determinants in the Theory of Estimation of Parameters of Some Systems....Pages 481-502
Random Determinants in Some Problems of Control Theory of Stochastic Systems....Pages 503-526
Random Determinants in Some Linear Stochastic Programming Problems....Pages 527-538
Random Determinants in General Statistical Analysis....Pages 539-587
Estimate of the Solution of the Kolmogorov-Wiener Filter....Pages 588-594
Random Determinants in Pattern Recognition....Pages 595-615
Random Determinants in the Experiment Design....Pages 616-626
Random Determinants in Physics....Pages 627-643
Random Determinants in Numerical Analysis....Pages 644-656
Back Matter....Pages 657-677
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