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.

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.


The copyright of all linked material rests with the author.

Commercial reproduction is prohibited, except as authorised by the author and publisher.