Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Near-maxima of the two-dimensional Discrete Gaussian Free Field   For the Discrete Gaussian Free Field (DGFF) in domains $D_N\subseteq\mathbb
Z^2$ arising, via scaling by $N$, from nice domains $D\subseteq\mathbb R^2$, we
study the statistics of the values order-$\sqrt{\log N}$ below the absolute
maximum. Encoded as a point process on $D\times\mathbb R$, the scaled spatial
distribution of these near-extremal level sets in $D_N$ and the field values
(in units of $\sqrt{\log N}$ below the absolute maximum) tends in law as
$N\to\infty$ to the product of the critical Liouville Quantum Gravity (cLQG)
$Z^D$ and the Rayleigh law. The convergence holds jointly with the extremal
process, for which $Z^D$ enters as the intensity measure of the limiting
Poisson point process, and that of the DGFF itself; the cLQG defined by the
limit field then coincides with $Z^D$. While the limit near-extremal process is
measurable with respect to the limit continuum GFF, the limit extremal process
is not. Our results explain why the various ways to "norm" the lattice cLQG
measure lead to the same limit object, modulo overall normalization.

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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: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
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The categories of this paper are: stat
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph