Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Causal Set-Continuum Correspondence   We present two results which concern certain aspects of the question: when is
a causal set well approximated by a Lorentzian manifold? The first result is a
theorem which shows that the number-volume correspondence, if required to hold
even for arbitrarily small regions, is best realized via Poisson sprinkling.
The second result concerns a family of lattices in $1+1$ dimensional Minkowski
space, known as Lorentzian lattices, which we show provide a much better
number-volume correspondence than Poisson sprinkling for large volumes. We
argue, however, that this feature should not persist in higher dimensions. We
conclude by conjecturing a form of the aforementioned theorem that holds under
weaker assumptions, namely that Poisson sprinkling provides the best
number-volume correspondence in $3+1$ dimensions for spacetime regions with
macroscopically large volumes.

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The categories of this paper are: solv-int
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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: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg