The Strange Logic of Random Graphs

2001
ISBN: 978-3-540-41654-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 22, 168 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 448 g

Reihe: Algorithms and Combinatorics

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.

Zielgruppe

Research

Autoren/Hrsg.

Spencer, Joel

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Mathematik | Informatik EDV | Informatik Informatik Logik, formale Sprachen, Automaten
• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik EDV | Informatik Informatik Theoretische Informatik

Inhaltsverzeichnis

I. Beginnings.- 0. Two Starting Examples.- 1. Preliminaries.- 2. The Ehrenfeucht Game.- II. Random Graphs.- 3. Very Sparse Graphs.- 4. The Combinatorics of Rooted Graphs.- 5. The Janson Inequality.- 6. The Main Theorem.- 7. Countable Models.- 8. Near Rational Powers of n.- III. Extras.- 9. A Dynamic View.- 10. Strings.- 11. Stronger Logics.- 12. Three Final Examples.