Probability on Graphs

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Juni 2010



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.


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.


Geoffrey Grimmett is Professor of Mathematical Statistics in the Statistical Laboratory at the University of Cambridge.


"It is written in a condensed style with only the briefest of introductions or motivations, but it is a mine of information for those who are well prepared and know how to use it. It formed the basis for a Probability reading group at the University of Warwick last term and was well received, and parts of it are being used by a colleague for an undergraduate module this term on Probability and Discrete Mathematics." R.S. MacKay, Contemporary Physics
EAN: 9780521147354
ISBN: 0521147352
Untertitel: Random Processes on Graphs and Lattices. 'Institute of Mathematical Statistics Textbooks'. 45 b/w illus. 90 exercises. Sprache: Englisch.
Verlag: Cambridge University Press
Erscheinungsdatum: Juni 2010
Seitenanzahl: 260 Seiten
Format: kartoniert
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