Résumé
The study of random graphs was begun by Paul Erdos and
Alfred Renyi in the 1960s and now has a comprehensive
literature. A compelling element has been the threshold
function, a short range in which events rapidly move from
almost certainly false to almost certainly true. This book
now joins the study of random graphs (and other random
discrete objects) with mathematical logic. The possible
threshold phenomena are studied for all statements
expressible in a given language. Often there is a zero-one
law, that every statement holds with probability near zero
or near one. The methodologies involve probability,
discrete structures and logic, with an emphasis on discrete
structures. The book will be of interest to graduate
students and researchers in discrete mathematics.
Contents
- Two starting examples
- Preliminaries
- The ehrenfeucht game
- Very sparse graphs
- The combinatorics of rooted graphs
- The janson inequality
- The main theorem
- Countable models
- Near rational powers of n
- A dynamic view
- Strings
- Stronger logics
- Three final examples
- Bibliography
- Index
Caractéristiques techniques
| PAPIER | |
| Éditeur(s) | Springer |
| Auteur(s) | Joel Spencer |
| Parution | 15/07/2001 |
| Nb. de pages | 168 |
| Format | 16 x 24 |
| Couverture | Relié |
| Poids | 385g |
| Intérieur | Noir et Blanc |
| EAN13 | 9783540416548 |
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