PIMS - UVic Dynamics and Probability Seminar: Gourab Ray

We prove that a well-known graphical expansion of the Ising model, known as the Loop O(1) model, is a factor of i.i.d. on unimodular random rooted graphs under various boundary conditions and in the presence of a non-negative 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. 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 prove and exploit is that the wired uniform spanning trees on unimodular transient graphs are factors of i.i.d. This partially answers some questions posed by Tom Hutchcroft.