Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Cram\'er--Wold device for infinite divisibility of
  $\mathbb{Z}^d$-valued distributions   We show that a Cram\'er--Wold device holds for infinite divisibility of
$\mathbb{Z}^d$-valued distributions, i.e. that the distribution of a
$\mathbb{Z}^d$-valued random vector $X$ is infinitely divisible if and only if
$\mathcal{L}(a^T X)$ is infinitely divisible for all $a\in \mathbb{R}^d$, and
that this in turn is equivalent to infinite divisibility of $\mathcal{L}(a^T
X)$ for all $a\in \mathbb{N}_0^d$. A key tool for proving this is a
L\'evy--Khintchine type representation with a signed L\'evy measure for the
characteristic function of a $\mathbb{Z}^d$-valued distribution, provided the
characteristic function is zero-free.

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The categories of this paper are: bayes-an
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
1
The categories of this paper are: cs
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The categories of this paper are: hep-th