Bay Area Discrete Math Day XII: Monotonicity in the Ising...

Google TechTalks Bay Area Discrete Math Day XII April 15, 2006 Nicholas Weininger (Google Inc.) ABSTRACT The Ising model assigns probabilities to "spin configurations" of the vertices of a graph G in which each vertex is given spin +1 or -1. In a ferromagnetic Ising model, for any v, w ∈V(G), setting the spin of v to +1 makes the spin at w more likely to be +1. A natural and elegant conjecture due to Kenyon, Mossel, and Peres states that the strength of this "influence" of v on w can only decrease when some other vertices' spins are fixed. We prove some partial results in this direction and discuss the obstacles to a full proof. We also discuss a related conjecture of Peres on a monotonicity...