Probability on Graphs
by Geoffrey Grimmett
These lecture notes have been prepared for students at the 2008 PIMS-UBC Summer School in Probability, for M2 students attending my course at the Institut Henri Poincaré, and for a Minerva Lecture course at Columbia University.
They are published by Cambridge University Press in 2010, as Volume 1 of the IMS Textbooks Series.
pdf file of July 2012, incorporating previous errata.
Theorem 3.14 should read: For any increasing random variable f: Omega \to R, the function etc...
Exercise 2.10. The answer should be 1/2.
Exercise 3.9. It is useful that theta(1/2)=0 for bond percolation on the square lattice, see Thm 5.33.
Exercise 5.4. Probably best to replace the first `greater than or equal to' by `less than or equal to'. Either would do for the first part, but the second part follows after the change.
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