UW-PIMS Mathematics Colloquium: Bela Bollobas

  • Date: 02/18/2011
  • Time: 14:30
Bela Bollobas

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

Other Information: 

Location: Raitt Hall, Room 121


For more information please visit University of Washington Department of Mathematics