Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of probability distribution convergence in Wasserstein
  distance by $L^{p}$-quantization error function   We establish conditions to characterize probability measures by their
$L^{p}$-quantization error functions in both $\mathbb{R}^{d}$ and Hilbert
settings. This characterization is two-fold: static (identity of two
distributions) and dynamic (convergence for the $L^p$-Wasserstein distance). We
first propose a criterion on the quantization level $N$, valid for any norm on
$\mathbb{R}^{d}$ and any order $p$ based on a geometrical approach involving
the Vorono\"i diagram. Then, we prove that in the $L^2$-case on a (separable)
Hilbert space, the condition on the level $N$ can be reduced to $N=2$, which is
optimal. More quantization based characterization cases on dimension 1 and a
discussion of the completeness of a distance defined by the quantization error
function can be found in the end of this paper.

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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: econ
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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: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex