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