Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the consistency and asymptotic normality of multiparameter persistent
  Betti numbers   The persistent Betti numbers are used in topological data analysis to infer
the scales at which topological features appear and disappear in the filtration
of a topological space. Most commonly by means of the corresponding barcode or
persistence diagram. While this approach to data science has been very
successful, it suffers from sensitivity to outliers, and it does not allow for
additional filtration parameters. Such parameters naturally appear when a cloud
of data points comes together with additional measurements taken at the
locations of the data. For these reasons, multiparameter persistent homology
has recently received significant attention. In particular, the multicover and
\v{C}ech bifiltration have been introduced to overcome the aforementioned
shortcomings.
  In this work, we establish the strong consistency and asymptotic normality of
the multiparameter persistent Betti numbers in growing domains. Our asymptotic
results are established for a general framework encompassing both the marked
\v{C}ech bifiltration, as well as the multicover bifiltration constructed on
the null model of an independently marked Poisson point process. In a
simulation study, we explain how the asymptotic normality can be used to derive
tests for the goodness of fit. The statistical power of such tests is
illustrated through different alternatives exhibiting more clustering, or more
repulsion than the null model.

10
The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
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The categories of this paper are: nlin
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The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
3
The categories of this paper are: physics
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cmp-lg