Probability on Graphs
(Sprache: Englisch)
Inspiration and provocation from a master expositor, taking you to the heart of contemporary probability. Grimmett's concise and masterful introduction to the basic mathematical ideas needed to model such random processes as viral marketing, epidemics,...
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Produktinformationen zu „Probability on Graphs “
Inspiration and provocation from a master expositor, taking you to the heart of contemporary probability. Grimmett's concise and masterful introduction to the basic mathematical ideas needed to model such random processes as viral marketing, epidemics, random algorithms, and efficient routing. The selection of topics and the approach taken to them is strongly motivated by modern applications. Each chapter ends with exciting exercises.
Klappentext zu „Probability on Graphs “
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. Schramm Löwner evolutions (SLE) arise in various contexts. The choice of topics is strongly motivated by modern applications and focuses on areas that merit further research. Special features include a simple account of Smirnov's proof of Cardy's formula for critical percolation, and a fairly full account of the theory of influence and sharp-thresholds. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Inhaltsverzeichnis zu „Probability on Graphs “
Preface; 1. Random walks on graphs; 2. Uniform spanning tree; 3. Percolation and self-avoiding walk; 4. Association and influence; 5. Further percolation; 6. Contact process; 7. Gibbs states; 8. Random-cluster model; 9. Quantum Ising model; 10. Interacting particle systems; 11. Random graphs; 12. Lorentz gas; References; Index.
Autoren-Porträt von Geoffrey R. Grimmett
Geoffrey Grimmett is Professor of Mathematical Statistics in the Statistical Laboratory at the University of Cambridge.
Bibliographische Angaben
- Autor: Geoffrey R. Grimmett
- 2010, 258 Seiten, 45 Abbildungen, Maße: 15 x 22,4 cm, Kartoniert (TB), Englisch
- Verlag: Cambridge University Press
- ISBN-10: 0521147352
- ISBN-13: 9780521147354
Sprache:
Englisch
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