Discrete Probability Models and Methods: Probability on Graphs and Trees, Markov Chains and Random Fields, Entropy and CodingThe emphasis in this book is placed on general models (Markov chains, random fields, random graphs), universal methods (the probabilistic method, the coupling method, the Stein-Chen method, martingale methods, the method of types) and versatile tools (Chernoff's bound, Hoeffding's inequality, Holley's inequality) whose domain of application extends far beyond the present text. Although the examples treated in the book relate to the possible applications, in the communication and computing sciences, in operations research and in physics, this book is in the first instance concerned with theory. The level of the book is that of a beginning graduate course. It is self-contained, the prerequisites consisting merely of basic calculus (series) and basic linear algebra (matrices). The reader is not assumed to be trained in probability since the first chapters give in considerable detail the background necessary to understand the rest of the book. |
Contents
| 1 | |
2 Random Variables | 20 |
3 Bounds and Inequalities | 65 |
4 Almost Sure Convergence | 78 |
5 The probabilistic Method | 93 |
6 Markov Chain Models | 117 |
7 Recurrence of Markov Chains | 145 |
8 Random Walks on Graphs | 184 |
14 Universal Source Coding | 356 |
15 Asymptotic Behaviour of Markov Chains | 373 |
16 The Coupling Method | 397 |
17 Martingale Methods | 416 |
18 Discrete Renewal Theory | 441 |
19 Monte Carlo | 457 |
20 Convergence Rates | 475 |
21 Exact Sampling | 509 |
9 Markov Fields on Graphs | 215 |
10 Random Graphs | 255 |
11 Coding Trees | 287 |
12 Shannons Capacity Theorem | 318 |
13 The Method of Types | 341 |
Appendix A | 535 |
| 545 | |
| 555 | |
Other editions - View all
Discrete Probability Models and Methods: Probability on Graphs and Trees ... Pierre Brémaud No preview available - 2018 |
Discrete Probability Models and Methods: Probability on Graphs and Trees ... Pierre Brémaud No preview available - 2017 |