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

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Published on October 9, 2007 3:15:31 AM ● Video Link: https://www.youtube.com/watch?v=h8Qfmg4WiEE

Duration: 24:03

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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...