Graphical representations of Ising as a factor of i.i.d.
Gourab Ray (University of Victoria)
Speaker 
Gourab Ray (University of Victoria)


When 
May 20, 2022
from 04:00 PM to 05:05 PM 
Where  zoom talk 
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Abstract: We prove that the Loop O(1) model, a wellknown graphical expansion of the Ising model, is a factor of i.i.d. on unimodular random rooted graphs under various conditions, including in the presence of a nonnegative external field. As an application we show that the gradient of the free Ising model is a factor of i.i.d. on unimodular planar maps having a locally finite dual. The key idea is to develop an appropriate theory of local limits of uniform even subgraphs with various boundary conditions and prove that they can be sampled as a factor of i.i.d. Another key tool we exploit is that the wired uniform spanning tree on a unimodular transient graph is a factor of i.i.d. This partially answers some questions posed by Hutchcroft.
I will finish with some related open questions, some of which are purely probabilistic and not related to factors of i.i.d.
Joint work with Omer Angel and Yinon Spinka.