'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.
Inhaltsverzeichnis
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 Stochastic 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 Stochastic Systems. - 22. Random Determinants in Some Linear Stochastic 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.
