Everything will be done ``from scratch'', so that the lectures are suitable for NON-EXPERTS; the only prerequisite is to have some familiarity with probability on the level that we usually require from first-year graduate students.
On the other hand, it is hoped that the lectures will also be of some interest to EXPERTS (such as those who attended the 1999 summer school on couplings), because most of the lectures will touch upon some recent twist, or at least on some material that was neither covered in the summer school, nor in the book by Lindvall (1992).
The lectures will be fairly independent of each other (although of course not totally devoid of cross-references), so those who wish can attend an arbitrary subset of them. However, graduate students are encouraged to attend the whole series, which in conjunction with some additional work will earn them 5 points in the graduate program; see the graduate course below.
Lectures will take place Fridays, 13:15-15:00 in room S1, starting on Friday, March 23. A more detailed scehdule is as follows.
March 23 | Lecture 1 | Coupling of Markov chains | |
March 30 | Lecture 2 | Coupling of random walks | |
April 6 | Lecture 3 | Coupling of renewal processes | |
April 9-20: Easter break. | |||
---|---|---|---|
April 27 | Lecture 4 | Some important inequalities: Holley, Harris and FKG | |
May 4 | Lecture 5 | Max-flow min-cut and Strassen's theorem on stochastic domination | |
May 11 | Lecture 6 | The Propp-Wilson algorithm with read-once randomness |
Presentations by participants are scheduled as follows.
Friday, May 18 | 13:15-15:00 | S1 | Nisse Dohrnér: Blackwell's renewal
theorem. Ulrica Olofsson: Schonmann's paper on uniqueness monotonicity in percolation. |
Wednesday, May 23 | 13:15-14:00 | S2 | Mats Kvarnström: Propp-Wilson algorithms for Markov random fields. |
Wednesday, May 30 | 13:15-16:00 | S2 | Kajsa Larsson: Fill's algorithm for perfect
simulation. Fredrik Lundin: Stochastic vs realizable monotonicity. Anders Muszta: Coupling and quantum physics. |
Wednesday, June 6 | 13:15-14:00 | S2 | Jenny Andersson: Spatial growth and competition. |