Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wasserstein Stability of the Entropy Power Inequality for Log-Concave
  Densities   We establish quantitative stability results for the entropy power inequality
(EPI). Specifically, we show that if uniformly log-concave densities nearly
saturate the EPI, then they must be close to Gaussian densities in the
quadratic Wasserstein distance. Further, if one of the densities is log-concave
and the other is Gaussian, then the deficit in the EPI can be controlled in
terms of the $L^1$-Wasserstein distance. As a counterpoint, an example shows
that the EPI can be unstable with respect to the quadratic Wasserstein distance
when densities are uniformly log-concave on sets of measure arbitrarily close
to one. Our stability results can be extended to non-log-concave densities,
provided certain regularity conditions are met. The proofs are based on optimal
transportation.

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The categories of this paper are: econ
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: chem-ph
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The categories of this paper are: cond-mat
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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: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga