Center for General Statistical Analysis and Theory of Random OperatorsDirected by Prof. Vyacheslav L. Girko 

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IntroductionThe Center for General Statistical Analysis was founded by Prof. Vyacheslav L. Girko in January 2000. The goals of the center are:

Contact informationInstitute of Mathematics
Email:agirko@i.com.ua 
Prof. Girko is editor of the following journals 
Statistical Analisis of Random Arrays (SARA) (in preparation) 
Staff and Editorial Board 

L. Accardi (Rome) 
S. Albeverio (Bochum) 
G. Cassati (Como) 
V. Kurotschka(Berlin) 
Y. Kondratyev (Bielefeld) 
I. Litvin(Port Elizabeth) 
H. Drygas (Kassel) 
N. Portenko (Kiev) 
N. Leonenko(Kardiff) 
A. Vladimirova (Kiev) 
A. F. Turbin (Kiev) 
I. Ibragimov (St. Petersburg) 
Yuri Krak (Kiev) 
S. Molchanov (Charlotte, NC) 
W. Kirsch (Bochum) 
N. Christopeit (Bonn) 
L. Pastur (Marsel) 
A. Klein (Irvine, CA) 
A. Shiryayev (Moscow) 
M. B. Malyutov (Boston) 
C. Domanski (Lodz) 
A. Rukhin (Baltimore) 
V. Fedorov (Tennessee) 
Muni S. Srivastava (Canada) 
E. Staffetti (Rome) 
E. Lebedev (Kiev) 
A. Babanin (Kiev) 
A. Nakonechny (Kiev) 
Ph. Loubaton (MarnelaVallee) 
R. Carmona (Princeton) 
Books 





Theory of Stochastic Canonical equations, Kluwer Academic Publishers, The Netherlands, 2001 
An Introduction to Statistical Analysis of Random Arrays. VSP, The Netherlands, 1998 
Multidimensional Statistical Analysis and Theory of Random Matrices. VSP, The Netherlands, 1996 
Theory of Random Determinants Kluwer Academic Publishers, The Netherlands, 1990 
Theory of Systems of Empirical Equations. "Lybid Publishing, Kiev, Ukraine, 1990 
Spectral Theory of Random Matrices. "Science" Publishing, Moscow, Russia, 1988 
Multidimensional Statistical Analysis. "Higher School" Publishing, Kiev, Ukraine, 1983 
Limit Theorems for Functions of Random Variables. "Higher School" Publishing, Kiev, Ukraine, 1983 
Theory of Random Determinants. Kiev University Publishing, Ukraine, 1975 
Random Matrices. Kiev University Publishing, Ukraine, 1975 
Recent Papers 
The Canonical Equation for the Resolvent of a Random Matrix with Asymptotically Independent Entries II. Random Operators and Stochastic Equations, V. 3, N.1, 1995, 4163 p. 
The Method of Random Determinants for Estimating the Permanent. Random Operators and Stochastic Equations, V. 3, N.2, 1995, 181193 p. 
Canonical Spectral Equation for the Empirical Covariance Matrices, Ukrainian Mathematical Journal , 1995, V. 47, N.9, 11761189 p. 
Elliptic Law: Ten Years Later I, Random Operators and Stochastic Equations, V. 3, N. 3, 1995, 257302 p. 
The Elliptic Law: Ten Years Later II, Random Operators and Stochastic Equations}, V. 3, N.4, 1995, 377398 p. 
Random Matrices, Handbook of Algebra. Elsevier Science B.V. 1995, 2778 p. 
Canonical Equation for Empirical Covariance Matrices. Proceedings of the 14th International Conference on Multivariate Statistical Analysis, MSA95, Warsaw, Poland, 1995, 225247 p. 
Minimax Estimators for Linear Models with Nonrandom Disturbances. Random Operators and Stochastic Equations V. 3, N.4, 1995, 361377 p. (with N. Christopeit). 
Spectral Theory of Minimax Estimation, Acta Applicandae Mathematicae V.3, 1996, 5969 p. 
The Canonical Spectral Equation, Theory of Probability and its Applications, V. 39, N.4, 1996, 685691 p. 
Canonical Equation for the Resolvent of Empirical Covariance Matrix, Random Operators and Stochastic Equations, V.4, N.1, 1996, 6176 p. 
Strong Law for the Eigenvalues and Eigenvectors of Empirical Covariance Matrices, Random Operators and Stochastic Equations, V.4, N.2, 1996, 179204 p. 
Multivariate Elliptically Contoured Linear Models and Some Aspects of the Theory of Random Matrices, "Multidimensional Statistical Analysis and Theory of Random Matrices". Proceedings of the Sixth Eugene Lukacs Symposium Held in Bowling Green State University, Department of Mathematics and Statistics, Bowling Green Ohio. Publishing VSP (with A.K. Gupta) 1996, 327387 p. 
Canonical equation for the resolvent of empirical covariance matrices pencil, "Multidimensional Statistical Analysis and Theory of Random Matrices". Proceedings of the Sixth Eugene Lukacs Symposium Held in Bowling Green State University, Department of Mathematics and Statistics, Bowling Green Ohio. Publishing VSP. (with A.K. Gupta), 1996, 4161 p. 
Strong Law for the eigenvalues of empirical covariance matrices. "Multidimensional Statistical Analysis and Theory of Random Matrices". Proceedings of the Sixth Eugene Lukacs Symposium Held in Bowling Green State University, Department of Mathematics and Statistics, Bowling Green Ohio. Publishing VSP. 1996, 6192 p. 
Distribution of spacings of random matrices. Part I: The First Spacing Law for Gaussian Hermitian matrices, Random Operators and Stochastic Equations V.4, N.3, 1996, 283300 p. 
Numerical and Monte Carlo Verification of the First Spacing Law, Random Operators and Stochastic Equations. V.4, N.4, 1996, 303314 p. (with N. Preston). 
A matrix equation for the resolvents of random matrices with independent blocks. Theory of Probability and its Applications, V.40, 4, 635644 (1996). 
Limit theorems for permanents. Theory of Probability and mathematical statistics, No. 53, 3342 (1996). 
Strong Law for the singular values and eigenvectors of random matrices, I. Random Operators and Stochastic Equations, V.5, N.1, 1997, 80104. 
Strong Circular Law. Random Operators and Stochastic Equations, V.5, N.2, 1997, 173197. 
Strong Elliptic Law. Random Operators and Stochastic Equations, V.5, N.3, 1997, 269306. 
The $V$density for eigenvalues of non symmetric random matrices and rigorous proof of the strong Circular law, Random Operators and Stochastic Equations, V.5, N.4, 371406 (1997). 
A Refinement of the central limit theorem for random determinants, Theory of Probability and Its Applications, V.42, N.1, 121129 (1997). 
Numerical and Monte Carlo Verification of the $V$Law, Random Operators and Stochastic Equations, V.6, N.2, 1998, 80104. (with R. Dias) 
Strong Law for the singular values and eigenvectors of random matrices II. Random Operators and Stochastic Equations, V.6, N.3, 1998, 291310. 
Convergence rate of the expected spectral functions of symmetric random matrices equals $O(n^{1/2})$. Random Operators and Stochastic Equations, V.6, N.4, 1998, 359406. 
The $V$relation between Hermitian and NonHermitian Operators and Strong Law for Normalized Spectral Functions of NonSelfadjoint Random Matrices with Independent Row Vectors. Markov Processes and Related Fields V.4, 4, 499508 (1998). 
Strong Law for the singular values and eigenvectors of random matrices III. Inequalities for the spectral radius of large random matrices, Random Operators and Stochastic Equations, V.7, N.2, 1999, 179200. 
Simulation of Eigenvalues of Random Matrices 

Numerical and Monte Carlo verification of Vdistribution 
Scientific Projects 
Proposition of a theory of optimization for obtaining minimax estimators of the parameters of the regression models 
The Development of Statistical Analysis of Random Arrays and Its Programm Applications 
The Main Law of the Theory of Random Matrices 
Wigner«s Semicircle Law 
Inverse Tangent Law 
The Logarithmic Law 
Ten Spacings Laws 
The Second Law for the Singular Values and Eigenvectors of Random Matrices 
The Third Law for the Eigenvalues and Eigenvectors of Empirical Covariance Matrices 
The Law of Large Numbers for the Product of Independent Random Matrices 
The Central Limit Theorem for the Product of Independent Random Matrices 
The Central Limit Theorem for the Resolvents of Random Matrices 
The Main Minimax Estimators 
The Main Estimators of GSA 
G1Estimator of Generalized Variance 
G2Estimator of Real Stieltjes Transform of the Normalized Spectral Function of Covariance Matrices 
G3Estimator of Inverse Covariance Matrix 
Class of G4Estimators for the Traces of the Powers of Covariance Matrices 
G5Estimator of Smoothed Normalized Spectral Function of Symmetric Matrices 
G6Estimator of Stieltjes' Transform of Covariance Matrix Pencil 
G7Estimator of the States of Discrete Control Systems 
Class of G8Estimators of the Solutions of Systems of Linear Algebraic Equations (SLAE) 
G9Estimator of the Solution of the Discrete KolmogorovWiener Filter 
G10Estimator of the Solution of a Regularized Discrete KolmogorovWiener Filter With Known Free Vector 
G11Estimator of the Mahalanobis Distance 
G12Regularized Mahalanobis Distance Estimator 
G13Discrimination of Two Populations With Common Unknown Covariance Matrix. G13AndersonFisher Statistics Estimator 
G14Estimator of Regularized Discriminat Function 
G15Estimator of the Nonlinear Discriminant Function, Obtaind by Observation of Random Vectors With Different Covariance Matrices 
G16Class of G1Estimators in the Theory of Experimental Desgn, When the Design Matrix is Unknown 
G17Estimate of T2Statistics 
G18Estimate of Regularized T2Statistics 
QuasiInversion Method for Solving $G$Equations 
Estimator $G {20}$ of Regularized Function of Unknown Parameters 
G21Estimator: Estimator in the Likelihood Method 