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Contraction of Measures on Graphs


Given a finitely supported probability measure μ on a connected graph G, we construct a family of probability measures interpolating the Dirac measure at some given point oG and μ. Inspired by Sturm-Lott-Villani theory of Ricci curvature bounds on measured length spaces, we then study the convexity of the entropy functional along such interpolations. Explicit results are given in three canonical cases, when the graph G is either ℤn, a cube or a tree.

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Correspondence to Erwan Hillion.

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Hillion, E. Contraction of Measures on Graphs. Potential Anal 41, 679–698 (2014).

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  • Ricci curvature
  • Sturm-Lott-Villani theory
  • Convexity of entropy
  • Measure contraction property

Mathematic Subject Classifications (2010)

  • 60B99
  • 05C99