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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