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Contraction of Measures on Graphs

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Abstract

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 o ∈ G 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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Authors and Affiliations

  1. Department of Mathematics, University of Luxembourg, Luxembourg, Grand Duchy of Luxembourg

    Erwan Hillion

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  1. Erwan Hillion
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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). https://doi.org/10.1007/s11118-014-9388-7

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  • DOI: https://doi.org/10.1007/s11118-014-9388-7

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