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.

pdf file of Second Edition, January 2018

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.

Errata to Second Edition

page 22: the edge e should be denoted f in the first paragraph.

page 198, equation (11.67): the term in p_0 should have a negative sign.

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