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  3. Probability on Graphs
  • Cited by 30
Publisher:
Cambridge University Press
Online publication date:
January 2018
Print publication year:
2018
Online ISBN:
9781108528986
DOI:
https://doi.org/10.1017/9781108528986
Subjects:
Physics and Astronomy, Abstract Analysis, Probability Theory and Stochastic Processes, General Statistics and Probability, Statistics and Probability, Statistical Physics
Series:
Institute of Mathematical Statistics Textbooks (8)
Information

Book description

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.

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