Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Boundedness of the nodal domains of additive Gaussian fields   We study the connectivity of the excursion sets of additive Gaussian fields,
i.e.\ stationary centred Gaussian fields whose covariance function decomposes
into a sum of terms that depend separately on the coordinates. Our main result
is that, under mild smoothness and correlation decay assumptions, the excursion
sets $\{f \le \ell\}$ of additive planar Gaussian fields are bounded almost
surely at the critical level $\ell_c = 0$. Since we do not assume positive
correlations, this provides the first examples of continuous
non-positively-correlated stationary planar Gaussian fields for which the
boundedness of the nodal domains has been confirmed. By contrast, in dimension
$d \ge 3$ the excursion sets have unbounded components at all levels.

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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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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: hep-ex
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The categories of this paper are: stat
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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: quant-ph