Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimers in piecewise Temperleyan domains   We study the large-scale behavior of the height function in the dimer model
on the square lattice. Richard Kenyon has shown that the fluctuations of the
height function on Temperleyan discretizations of a planar domain converge in
the scaling limit (as the mesh size tends to zero) to the Gaussian Free Field
with Dirichlet boundary conditions. We extend Kenyon's result to a more general
class of discretizations.
  Moreover, we introduce a new factorization of the coupling function of the
double-dimer model into two discrete holomorphic functions, which are similar
to discrete fermions defined in [Stas, Stas07].For Temperleyan discretizations
with appropriate boundary modifications, the results of Kenyon imply that the
expectation of the double-dimer height function converges to a harmonic
function in the scaling limit. We use the above factorization to extend this
result to the class of all polygonal discretizations, that are not necessarily
Temperleyan. Furthermore, we show that, quite surprisingly, the expectation of
the double-dimer height function in the Temperleyan case is exactly discrete
harmonic (for an appropriate choice of Laplacian) even before taking the
scaling limit.

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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: eess