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Probability on Graphs: Random Processes on Graphs and Lattices

Geoffrey Grimmett
Publisher: 
Cambridge University Press
Publication Date: 
2018
Number of Pages: 
265
Format: 
Paperback
Series: 
IMS Textbooks
Price: 
34.99
ISBN: 
9781108438179
Category: 
Textbook
[Reviewed by
Fernando Q. Gouvêa
, on
01/30/2018
]

See Miklós Bóna’s review of the first edition. Beyond the usual minor changes and improvements, the author tells us that several major additions have been made:

  • “a proof of the connective constant of the hexagonal lattice”
  • “an improved influence theorem for general product spaces”
  • “a streamlined proof of exponential decay for subcritical percolation”
  • “a proof of the critical point of the random-cluster model on the square lattice”

This is clearly a successful advanced textbook.


Fernando Q. Gouvêa is the editor of MAA Reviews.

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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