# Probability on Graphs, Second Edition 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.

This Second Edition is published by Cambridge University Press in 2018, as Volume 8 of the IMS Textbooks Series.

Errata to First Edition

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.