We will investigate objects such as: random permutations, random functions, random trees, random graphs, random walks (on fixed graphs).
Time permitting, we will say something about more sophisticated topics, e.g. percolations and random matrices.
Read Chapter 3 of [Percolation, Bollobas and Riordan]
(you will need some definitions from Chapter 1, as well). Or, have a look at the arxiv for a journal version of the same material.
Then sketch a proof for the main theorem proven there: that $p_H(\Z^2)=1/2$.
Be precise in statements, but you may skip details of the proof, as long as you state precisely what was not proven. Keep it below 5-6 pages.
To be handed in by September 31.
Last updated: 20 Aug 2008