Title: Random geometry and percolation.
Course description: This is a graduate topics course in probability theory.
In this course we will learn about percolation on lattices and other
graphs, phase transitions, isoperimetry of graphs and connections to random
walks on graphs, and correlated percolation models such as Random
Interlacements and the Gaussian free field.
Text books: (last two books are free from Springerlink, when connected
through the university)
1. Grimmett - Percolation 2nd edition.
2. Drewitz, Rath and Sapozhnikov - An introduction to random
interlacements. (http://link.springer.com/book/10.1007/978-3-319-05852-8)
3. Benjamini - Coarse Geometry and randomness. (
http://link.springer.com/book/10.1007/978-3-319-02576-6)
For partial lecture notes (not including correlated percolation models) see
https://www.dropbox.com/s/8e8m2j627hp8ygf/Percolation%20and%20random%20geometry.pdf?dl=0