Probability on Graphs

2. Auflage 2018
ISBN: 978-1-108-43817-9
Verlag: Cambridge University Press

Buch, Englisch, Band 8, 276 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 407 g

Reihe: Institute of Mathematical Statistics Textbooks

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. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. 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.

Autoren/Hrsg.

Grimmett, Geoffrey

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

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.

Über Autor(innen)

Grimmett, Geoffrey
Geoffrey Grimmett is Professor of Mathematical Statistics in the Statistical Laboratory at the University of Cambridge. He has written numerous research articles in probability theory, as well as popular research books on percolation and the random-cluster model. In addition, he is a co-author, along with David Stirzaker and Dominic Welsh, of two successful textbooks on probability and random processes at the undergraduate and postgraduate levels. He has served as Master of Downing College since 2013 and was elected to the Royal Society in 2014.