Theory of Stochastic Canonical Equations: Volumes I and 2

Front Matter....Pages i-xlix
Canonical Equation K 1 ....Pages 1-24
Canonical Equation K 2 . Necessary and Sufficient Modified Lindeberg’s Condition. The Wigner and Cubic Laws....Pages 25-50
Regularized Stochastic Canonical Equation K 3 for Symmetric Random Matrices with Infinitely Small Entries....Pages 51-74
Stochastic Canonical Equation K 4 for Symmetric Random Matrices with Infinitely Small Entries. Necessary and Sufficient Conditions for the Convergence of Normalized Spectral Functions....Pages 75-86
Canonical Equation K 5 for Symmetric Random Matrices with Infinitely Small Entries....Pages 87-92
Canonical Equation K 6 for Symmetric Random Matrices with Identically Distributed Entries....Pages 93-96
Canonical Equation K 7 for Gram Random Matrices....Pages 97-118
Canonical Equation K 8 ....Pages 119-124
Canonical Equation K 9 for Random Matrices whose Entries have Identical Variances....Pages 125-128
Canonical Equation K 10 . Necessary and Sufficient Modified Lindeberg Condition....Pages 129-140
Canonical Equation K 11 . Limit Theorem for Normalized Spectral Functions of Empirical Covariance Matrices under the Modified Lindeberg Condition....Pages 141-152
Canonical Equation K 12 for Random Gram Matrices with Infinitely Small Entries....Pages 153-160
Canonical Equation K 13 for Random Gram Matrices with Infinitely Small Entries....Pages 161-164
The Method of Random Determinants for Estimating the Permanents of Matrices and the Canonical Equation K 14 for Random Gram Matrices....Pages 165-180
Canonical Equation K 15 for Random Gram Matrices with Identically Distributed Entries....Pages 181-184
Canonical Equation K 16 for Sample Covariance Matrices....Pages 185-202
Canonical Equation K 17 for Identically Distributed Independent Vector Observations and the G 2 -Estimators of the Real Stieltjes Transforms of the Normalized Spectral Functions of the Covariance Matrices....Pages 203-206
Canonical Equation K 18 for the Special Structure of Vector Observations....Pages 207-224
Canonical Equation K 19 ....Pages 225-230
Canonical Equation K 20 . Strong Law for Normalized Spectral Functions of Nonselfadjoint Random Matrices with Independent Row Vectors. Simple Rigorous Proof of the Strong Circular Law....Pages 231-260
Canonical Equation K 21 for Random Matrices with Independent Pairs of Entries with Zero Expectations. Circular and Elliptic Laws....Pages 261-322
Canonical Equation K 22 for Random Matrices with Independent Pairs of Entries....Pages 323-354
Canonical Equation K 23 for Random Matrices with Independent Pairs of Entries with Different Variances and Equal Covariances....Pages 355-358
Canonical Equation K 24 for Random G -Matrices with Infinitesimally Small Random Entries....Pages 359-364
Canonical Equation K 25 for Random G -Matrices. Strong V -Law....Pages 365-382
Class of Canonical V -Equations K 26 for a Single Matrix and a Product of Two Random Matrices. The V -Density of Eigenvalues of Random Matrices such that the Variances of their Entries Form a Doubly Stochastic Matrix....Pages 383-400
Canonical Equation K 27 for Normalized Spectral Functions of Random Symmetric Block Matrices....Pages 401-424
Canonical Equation K 28 for Normalized Spectral Functions of Random Symmetric Matrices with Identically Distributed Independent Blocks. Block Matrix Density. SS -Laws....Pages 425-430
Canonical Equation K 29 for the Fourier Transform of the Resolvent of a Symmetric Block Random Matrix....Pages 431-438
Canonical Equation K 30 for Normalized Spectral Functions of Random Gram Block Matrices....Pages 439-462
Canonical Equation K 31 for Normalized Spectral Functions of the Sum of Random Gram Matrix and Nonrandom Matrix....Pages 464-471
Canonical Equation K 32 for Normalized Spectral Functions of Random Gram Matrices with Identically Distributed Independent Blocks. Block Matrix Density....Pages 472-477
Canonical Equation K 33 for the Fourier Transform of the Resolvent of a Gram Block Random Matrix....Pages 478-487
Canonical Equation K 34 for Normalized Spectral Functions of Empirical Covariance Matrix with Asymptotically Independent Blocks....Pages 488-495
Canonical Equation K 35 for Normalized Spectral Functions of a Pencil of Random Matrices....Pages 496-507
Canonical Equation K 36 for Normalized Spectral Functions of a Pencil of Random Matrices....Pages 508-515
Canonical Equation K 37 for Normalized Spectral Functions of a Pencil of Empirical Random Matrices....Pages 516-519
Canonical Equation K 38 for Normalized Spectral Functions of a Pencil of Random Nonsymmetric Matrices. G-Law....Pages 520-531
Twenty Five Years of Stochastic Canonical Equation K 39 for Normalized Spectral Functions of Ace-Symmetric Matrices....Pages 532-565
Twenty Five Years of Stochastic Canonical Equation K 40 for Normalized Spectral Functions of Ace-Gram Matrices....Pages 566-621
Stochastic Canonical Equation K 41 for Normalized Spectral Functions of Empirical Covariance Matrices....Pages 622-625
Stochastic Canonical Equation K 42 for Normalized Spectral Functions of Random Symmetric Matrices with Block Structure....Pages 626-631
Stochastic Canonical Equation K 43 for Normalized Spectral Functions of Random Gram Block Matrices....Pages 632-635
Stochastic Canonical Equation K 44 for Normalized Spectral Functions of Empirical Covariance Matrices with Block Structure....Pages 636-639
Stochastic Canonical Equation K 45 for Normalized Spectral Functions of Random Matrices Pencil....Pages 640-649
Canonical Equation K 46 for the Stieltjes Transform of Normalized Spectral Functions of Tridiagonal and Jacobi Random Matrices....Pages 650-665
Class of Direct Canonical Equations K 47 for Spectral Functions of Random Symmetric Banded Matrices and Jacobi Matrices....Pages 666-677
Canonical Equation K 48 for Normalized Spectral Functions of a Product of Random Matrices....Pages 678-681
Canonical Equation K 49 for Normalized Spectral Functions of a Product of Random Unitary Matrices....Pages 682-687
Class of Canonical Equations K 50 for the Entries of Random S -Matrices....Pages 688-699
Canonical Equation K 51 for Normalized Spectral Functions of a Product of Random Independent Matrices....Pages 700-713
Canonical Equation K 52 for Hankel and Toeplitz Random Matrices....Pages 714-727
The Class of Canonical Equations K 53 for the Solutions of the System of Linear Algebraic Equations with Random Coefficients. Inverse Tangent and Canonical Laws....Pages 728-773
Canonical Equation K 54 for Normalized Spectral Functions of Nonself-Adjoint Random Jacobi Matrices....Pages 774-801
Canonical Equation K 55 for Normalized Spectral Functions of a Product of Two Independent Nonsymmetric Random Matrices....Pages 802-813
Canonical Equation K 56 for the Solution of the System of Linear Differential Equations with Random Coefficients....Pages 814-827
Canonical Equation K 57 , the Cubic Law, the Invariance Principle and Related Topics in the Theory of Analytic Functions of Random Matrices....Pages 828-855
Canonical Equation K 58 . Universality and Arcsine Laws for Random Matrices A + U m B ( U *) m ....Pages 856-877
Canonical Equation K 59 and Universality Law for Random Matrices ( A + UB )( A + UB )*. Arcsine Law....Pages 878-895
Back Matter....Pages 896-961