Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gibbs Ensembles of Nonintersecting Paths   We consider a family of determinantal random point processes on the
two-dimensional lattice and prove that members of our family can be interpreted
as a kind of Gibbs ensembles of nonintersecting paths. Examples include
probability measures on lozenge and domino tilings of the plane, some of which
are non-translation-invariant.
  The correlation kernels of our processes can be viewed as extensions of the
discrete sine kernel, and we show that the Gibbs property is a consequence of
simple linear relations satisfied by these kernels. The processes depend on
infinitely many parameters, which are closely related to parametrization of
totally positive Toeplitz matrices.

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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: adap-org
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex