Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ricci curvature of finite Markov chains via convexity of the entropy   We study a new notion of Ricci curvature that applies to Markov chains on
discrete spaces. This notion relies on geodesic convexity of the entropy and is
analogous to the one introduced by Lott, Sturm, and Villani for geodesic
measure spaces. In order to apply to the discrete setting, the role of the
Wasserstein metric is taken over by a different metric, having the property
that continuous time Markov chains are gradient flows of the entropy.
  Using this notion of Ricci curvature we prove discrete analogues of
fundamental results by Bakry--Emery and Otto--Villani. Furthermore we show that
Ricci curvature bounds are preserved under tensorisation. As a special case we
obtain the sharp Ricci curvature lower bound for the discrete hypercube.

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The categories of this paper are: hep-ex
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The categories of this paper are: eess
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The categories of this paper are: stat
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math-ph