Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Asymptotic Faber-Krahn Inequality for the Combinatorial Laplacian on
  Z^2   The Faber-Krahn inequality states that among all open domains with a fixed
volume in R^n, the ball minimizes the first Dirichlet eigenvalue of the
Laplacian. We study an asymptotic discrete analogue of this for the
combinatorial Dirichlet Laplacian acting on induced subgraphs of Z^2. Namely,
an induced subgraph G with n vertices is called a minimizing subgraph if it
minimizes the first eigenvalue of the combinatorial Dirichlet Laplacian among
all induced subgraphs with n vertices. Consider an induced subgraph G and take
the interior of the union of closed squares of area 1 about each point of G.
Let G* denote this domain scaled down to have area 1. Our main theorem states
that if {G_n} is a sequence of minimizing subgraphs where each G_n has n
vertices, then after translation the measure of the symmetric difference of
G_n* and the unit disk converges to 0.

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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: nucl-th
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph