*Tid:***27 september 1999 kl 1515-1700 **

*Plats :***Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:***
Johan Jonasson,
Matematisk statistik,
Chalmers Tekniska Högskola.
Publikationslista (List of Publications).
**

**Titel:** **
My three favorite proofs and some related open problems.
**

*Sammanfattning: *

1. Matthews' theorem on the cover time for a simple random walk on a finite graph: Let denote the time taken for a random walk starting from to hit . Set and and let denote the cover time, i.e the time taken for a random walk starting from to visit every vertex of the graph. Then for any , where is the number of vertices in the graph.

2. To properly mix a deck of cards using the ordinary riffle shuffle, shuffles suffices.

3. The exact critical value for iid percolation on the triangular lattice is .

In connection to these results we also give some examples of intriguing open problems.