## UW-PIMS Mathematics Colloquium: Bela Bollobas

- Date: 02/18/2011
- Time: 14:30

University of Washington

The critical probability of percolation. Percolation on self-dual polygon configurations

In this talk I shall sketch some results Oliver Riordan of Oxford and I have

obtained on critical probabilities in percolation.

Recently, Scullard and Ziff noticed that a broad class of planar percolation

models are self-dual under a simple condition which, in a parametrized

version of such a model, reduces to a single equation. They stated that the

solution of the resulting equation gave the critical point. However, just as

in the classical case of bond percolation on the square lattice, noticing

self-duality is simply the starting point: the mathematical difficulty is

precisely showing that self-duality implies criticality. Riordan and I have

managed to overcome this difficulty: we have shown that for a generalization

of the models considered by Scullard and Ziff self-duality indeed implies

criticality.

Location: Raitt Hall, Room 121

For more information please visit University of Washington Department of Mathematics