Article (Scientific journals)
Contraction of Measures on Graphs
HILLION, Erwan
2014In Potential Analysis, 41, p. 679--698
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Keywords :
Ricci curvature; Sturm-Lott-Villani theory; Convexity of entropy
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
HILLION, Erwan ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
Contraction of Measures on Graphs
Publication date :
2014
Journal title :
Potential Analysis
ISSN :
0926-2601
eISSN :
1572-929X
Publisher :
Springer, Amsterdam, Netherlands
Volume :
41
Pages :
679--698
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 26 January 2015

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