Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On nonexpansiveness of metric projection operators on Wasserstein spaces   In this note we investigate properties of metric projection operators onto
closed and geodesically convex proper subsets of Wasserstein spaces
$(\mathcal{P}_p(\mathbf{R}^d),W_p).$ In our study we focus on the particular
subset of probability measures having densities uniformly bounded by a given
constant. When $d=1$, $(\mathcal{P}_2(\mathbf{R}),W_2)$ is isometrically
isomorphic to a flat space with a Hilbertian structure, and so the
corresponding projection operators are nonexpansive. We prove a general "weak
nonexpansiveness" property in arbitrary dimension which provides (among other
things) a direct proof of nonexpansiveness when $d=1$. When $d>1$, the space
$(\mathcal{P}_2(\mathbf{R}^d),W_2)$ is non-negatively curved in the sense of
Alexandrov. So, the question of nonexpansiveness of projection operators on
$(\mathcal{P}_p(\mathbf{R}^d),W_p)$ is more subtle. We show the failure of this
property for $p\in (1,p(d))$ and we give a quantitative asymptotic estimate on
$p(d)>1$ as $d \to \infty$. This result provides a heuristic argument for the
non-negative curvature of $(\mathcal{P}_p(\mathbf{R}^d),W_p)$ when $p\in
(1,p(d))$. Further geometric properties of independent interest are also
discussed.

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The categories of this paper are: econ
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: eess
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The categories of this paper are: atom-ph
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin