A Survey of the Early History of the Theory of Random Mappings

Kapitel in diesem Buch

1. Frontmatter I
2. CONTENTS V
3. Preface IX
4. A Survey of the Early History of the Theory of Random Mappings 1
5. On Goncharov's Works in the Field of Combinatorics 23
6. Probability Distributions in Prime Number Theory 28
7. Polynomial and Polynomial-Like Allocations: Recent Developments 40
8. Properties of Random Permutations with Constraints on the Maximum Cycle Length 60
9. Stochastic Properties of Systems of Random Linear Equations over Finite Algebraic Structures 64
10. On the Number of Solutions of Systems of Pseudo-Boolean Random Equations 71
11. Problems of Security in Information Processing Systems 99
12. Decomposable Statistics Based on the Spacings and Spacing-Frequencies of Higher Orders 128
13. On the Allocation Processes with Given Distributions of Frequency Vectors 133
14. Statistical Problems Concerned with Estimation of the Composition of β-Radioactive Wastes 143
15. On Transient Phenomena for Branching Migration Processes 148
16. Asymptotic Behaviour of Waiting Times in a Scheme of Particle Allocation 155
17. Limit Theorems for U-Statistics of Dependent Random Variables 186
18. Limit Theorems for Decomposable Statistics of Dependent Random Variables 200
19. Estimating Finite Stratified Population 212
20. Asymptotic Expansions for Permutation Tests with Several Samples 226
21. On Approximation of Weighted Sums of Random Variables with Two-Dimensional Indices 240
22. On a Lower Bound for the Isoperimetric Number of Cubic Graphs 251
23. A Risk Function in Global Optimization Problem 266
24. On an Existence Theorem for Decomposable Statistics 271
25. The Propriety of Phase Transitions in Random Graphs 287
26. On Sums of Values of the Legendre Symbol over Components in a Scheme of Generation of Random Vectors 298
27. On the Strong Law of Large Numbers for Sums of Pairwise Independent Random Variables 305
28. On a Special Class of Functions Associated with the Complexity of String Correction Problem 313
29. Operator Moments of Random Euclidean Mappings 316
30. Percolation Method in a System of Numerous Particles 329
31. Models of ρ-Percolation 337
32. On Estimation of the Coefficient of Asymptotic Relative Efficiency of Discrete-Analogue Algorithms to Detect Signals in a Non-Gaussian Noise 348
33. Random Mappings and Trees: Relations between Asymptotics of Moments of Certain Characteristics 353
34. On a Nonlinear Generalization of the Occupancy Problem 366
35. Weak Convergence of Certain Multiple Sums of Dependent Random Variables 376
36. On Problems of Renewal System Theory for Finite Time Interval 386
37. On the Generating Functions of Coloured Partitions and Limit Theorems for Sums of Indicators 395
38. Probabilistic Methods in the Theory of Approximation of Discrete Functions 403
39. Chernoff's Inequality for Sum of Independent Random Vectors 413
40. Some Limit Theorems in Batch Allocation Scheme with Random Levels Defined by an Allocation Scheme 428
41. Runs in Finite Markov Chains 437
42. How Often is Addition Equal to Bitwise Addition? 451
43. Boolean Functions and Approximation of Vectors 454
44. Limit Theorems for Random A-Permutations 459
45. LIST OF CONTRIBUTORS 470
46. ORGANIZING COMMITTEE 470