Probability on graphs : random processes on graphs and lattices / Geoffrey Grimmett, Statistical Laboratory, University of Cambridge.
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,...
Saved in:
| Online Access: |
Full Text (via Cambridge) |
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| Main Author: | |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge ; New York, NY :
Cambridge University Press,
[2018]
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| Edition: | Second edition. |
| Series: | Institute of Mathematical Statistics textbooks ;
8. |
| Subjects: |
| Summary: | 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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| Physical Description: | 1 online resource (xi, 265 pages) |
| Bibliography: | Includes bibliographical references and index. |
| ISBN: | 9781108528986 1108528988 |
| DOI: | 10.1017/9781108528986 |
| Source of Description, Etc. Note: | Print version record. |