Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform even subgraphs and graphical representations of Ising as factors
  of i.i.d   We prove that the Loop O(1) model, a well-known 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 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 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 prove and 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.

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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
1
The categories of this paper are: cs
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph