Graduate Seminar

Chris Potter
Carnegie Mellon University
Title: The random-cluster model of Fortuin & Kasteleyn

Abstract: In earlier presentations at GSS I've introduced and analyzed several algorithms for solving (or at least estimating statistical properties of) the Ising model and Potts models of the magnetic interaction of ferromagnetic crystals. Some of those algorithms made use of the fact that the Ising model can be recast as a percolation problem.

In this presentation, I will go through the main points of the groundbreaking 1971 result due to Fortuin and Kasteleyn (of the now-famous Kasteleyn signings) which provides the mathematical background for this fortuitous relationship. In fact, the "random-cluster model" defined in that paper has not only the Ising and percolation models as special cases, but also some graph coloring problems and the problem of deducing current on each segment of a linear electrical network.

Date: Thursday, February 28, 2013
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Brian Kell