Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From Super Poincar\'e to Weighted Log-Sobolev and Entropy-Cost
  Inequalities   We derive weighted log-Sobolev inequalities from a class of super Poincar\'e
inequalities. As an application, the Talagrand inequality with larger distances
are obtained. In particular, on a complete connected Riemannian manifold, we
prove that the $\log^\dd$-Sobolev inequality with $\dd\in (1,2)$ implies the
$L^{2/(2-\dd)}$-transportation cost inequality
  $$W^\rr_{2/(2-\dd)}(f\mu,\mu)^{2/(2-\dd)}\le C\mu(f\log f), \mu(f)=1, f\ge
0$$ for some constant $C>0$, and they are equivalent if the curvature of the
corresponding generator is bounded below. Weighted log-Sobolev and entropy-cost
inequalities are also derived for a large class of probability measures on
$\R^d$.

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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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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: stat
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg