Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Factor-of-iid Schreier decorations of lattices in Euclidean spaces   A Schreier decoration is a combinatorial coding of an action of the free
group $F_d$ on the vertex set of a $2d$-regular graph. We investigate whether a
Schreier decoration exists on various countably infinite transitive graphs as a
factor of iid.
  We show that $\mathbb{Z}^d,d\geq3$, the square lattice and also the three
other Archimedean lattices of even degree have finitary-factor-of-iid Schreier
decorations, and exhibit examples of transitive graphs of arbitrary even degree
in which obtaining such a decoration as a factor of iid is impossible.
  We also prove that symmetrical planar lattices with all degrees even have a
factor of iid balanced orientation, meaning the indegree of every vertex is
equal to its outdegree, and demonstrate that the property of having a
factor-of-iid balanced orientation is not invariant under quasi-isometry.

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The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci