Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete Balayage and Boundary Sandpile   We introduce a new lattice growth model, which we call boundary sandpile. The
model amounts to potential-theoretic redistribution of a given initial mass on
$\mathbb{Z}^d$ ($d\geq 2$) onto the boundary of an (a priori) unknown domain.
The latter evolves through sandpile dynamics, and has the property that the
mass on the boundary is forced to stay below a prescribed threshold. Since
finding the domain is part of the problem, the redistribution process is a
discrete model of a free boundary problem, whose continuum limit is yet to be
understood.
  We prove general results concerning our model. These include canonical
representation of the model in terms of the smallest super-solution among a
certain class of functions, uniform Lipschitz regularity of the scaled odometer
function, and hence the convergence of a subsequence of the odometer and the
visited sites, discrete symmetry properties, as well as directional
monotonicity of the odometer function. The latter (in part) implies the
Lipschitz regularity of the free boundary of the sandpile.
  As a direct application of some of the methods developed in this paper,
combined with earlier results on classical Abelian sandpile, we show that the
boundary of the scaling limit of Abelian sandpile is locally a Lipschitz graph.

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The categories of this paper are: stat
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The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin