Ph.D. course on

Percolation Theory

January-March 2012

During January-March 2012, I (Olle Häggström) am giving a Ph.D. course on percolation theory at the Depratment of Mathematical Sciences at Chalmers/GU. In order to be able to move quickly from the very basics to (certain parts of) the research front in this lively branch of probability theory, the course will be based not on a book but mostly on survey papers. The default format will be that the course will give 7.5 hp credits, but ambitious students may choose to expand the material covered by the examination in various directions and receive a bigger reward in terms of hp credits.

The exam will be a combination of written and oral examination. (More or less, the oral part will be your chance to defend your written solutions.) The exam will take place on Monday, April 2, at 8.30-11.30. The material that you are expected to defend at the exam is as follows:

Following are the lecture times I've scheduled for the course.

Tuesday, January 17 08.00-09.45MVL14 The basics of bond percolation on the square lattice: p 2-8 of Steif (2009).
Thursday, January 19 08.00-09.45MVL14 Ergodic theoretic preparations for, and beginning of, the spectacular 8-page paper by Harris (1960) who showed that for bond percolation on Z2 at the self-dual point p=1/2, there is no infinite cluster, so that pc≥1/2.
Tuesday, January 24 08.00-09.45MVL14 Harris (1960), continued.
Tuesday, January 31 08.00-09.45MVL14 Harris' inequality, as treated by Häggström (2007).
Thursday, February 2 08.00-09.45MVL14 Percolation and the Ising model, based on Sections 1-2 in Häggström (1998).
Tuesday, February 14 08.00-09.45MVL14 More on percolation and the Ising model, based on Sections 2-3 in Häggström (1998).
Tuesday, February 21 08.00-09.45MVL14 1. Some final remarks on the Ising model (Section 3 in Häggström, 1998).
2. Uniqueness of the infinite cluster in percolation models (Sections 1-2 in Häggström and Jonasson, 2006).
Thursday, February 23 08.00-09.45MVL14 Percolation on trees, loosely based on Section 5 of Steif (2009).
Friday, March 2 Note: change of day! 08.00-09.45MVL14 Percolation on the Grimmett-Newman graph, based loosely on Section 4 in Häggström and Jonasson (2006).
Tuesday, March 6 08.00-09.45MVL14 Uniqueness monotonicity and mass transport, based on Section 3 in Häggström (2011) and Section 5 in Häggström and Jonasson (2006).
Thursday, March 8 08.00-09.45MVL14 Uniqueness for p close to 1 using cluster frequency, based on Section 8 in Häggström and Jonasson (2006).
Thursday, March 15 08.00-09.45MVL14 More on percolation and (non-)amenability, based on Section 3 in Häggström (2011).
Thursday, March 22 08.00-09.45MVL14 Percolation on nonamenable graphs at criticality, based on Section 4 in Häggström (2011).
Monday, April 2 08.30-11.30 MVL14EXAM!