Probability on graphs : random processes on graphs and lattices
著者
書誌事項
Probability on graphs : random processes on graphs and lattices
（Institute of Mathematical Statistics textbooks, 1）
Cambridge University Press, 2010
- : hbk
- : pbk
大学図書館所蔵 件 / 全36件
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: hbk415.7/G 86031212015004043,
: hbk.GRIM/10/6033212010002541, : pbk.GRIM/10/6A033212015500632 -
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注記
Includes bibliographical references (p. 226-242) and index
内容説明・目次
内容説明
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-Loewner 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.
目次
- 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.
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