Theory of Random Determinants [Paperback]

1. Generalized Wishart Density and Integral Representation for Determinants.- ?1. The Haar Measure.- ?2. The Haar Measure On the Group of Orthogonal Matrices.- ?3. The Generalized Wishart Density.- ?4. Integral Representations for Determinants.- ?5. Integration on Grassmann and Clifford Algebras.- 2. Moments of Random Matrix Determinants.- ?1. Moments of Random Gram Matrix Determinants.- ?2. Moments of Random Vandermond Determinants. Hypothesis by Mehta and Dyson.- ?3. Methods of Calculating the Moments of Random Determinants.- ?4. Moments of Random Permanents.- ?5. Formulas of Random Determinant Perturbation.- 3. Distribution of Eigenvalues and Eigenvectors of Random Matrices.- ?1. Distribution of Eigenvalues and Eigenvectors of Hermitian Random Matrices.- ?2. Distribution of the Eigenvalues and Eigenvectors of Antisymmetric Random Matrices.- ?3. Distribution of Eigenvalues and Eigenvectors of Nonsymmetric Random Matrices.- ?4. Distribution of the Eigenvalues and Eigenvectors of Complex Random Matrices.- ?5. Distribution of Eigenvalues of Gaussian Real Random Matrices.- ?6. Distribution of Eigenvalues and Eigenvectors of Unitary Random Matrices.- ?7. Distribution of Eigenvalues and Eigenvectors of Orthogonal Random Matrices.- ?8. Distribution of Roots of Algebraic Equations with Random Coefficients.- 4. Inequalities for Random Determinants.- ?1. The Stochastic Hadamard Inequality.- ?2. Inequalities for Random Determinants.- ?3. The Frechet Hypothesis.- ?4.On Inequalities for Sums of the Martingale Difference and Random Quadratic Forms.- 5. Limit Theorems for the Borel Functions of Independent Random Variables.- ?1. Limit Theorems with the Lindeberg Condition.- ?2. Limit Theorems for Polynomial Functions of Independent Random Variables.- ?3. Accompanying Infinitely Divisible Distributions for Borel Functions of Independent Random Variables.- ?4. Limit Theorems for Sums of Martingale Differences.- ?5. Limit Theorems for Sums of Martingale Differences in Nonclassical ls3