Reference : Contraction of Measures on Graphs
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/19716
Contraction of Measures on Graphs
English
Hillion, Erwan mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
2014
Potential Analysis
Springer
41
679--698
Yes (verified by ORBilu)
International
0926-2601
1572-929X
Amsterdam
The Netherlands
[en] Ricci curvature ; Sturm-Lott-Villani theory ; Convexity of entropy
[en] 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 Z^n , a cube or a tree.
http://hdl.handle.net/10993/19716
10.1007/s11118-014-9388-7
http://link.springer.com/article/10.1007%2Fs11118-014-9388-7

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