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.