Geodesic
The Ricci Curvature of a Weighted Tree
Matematičeskie zametki, Tome 100 (2016) no. 4, pp. 586-596

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An expression for the coarse Ricci curvature of a weighted tree with a random walk on the vertex set is obtained. As a corollary, it is shown that the structure of a binary tree can be reconstructed up to isomorphism from the matrix of pairwise Ricci curvatures of its vertices.
Keywords: weighted tree, Ricci curvature, coarse Ricci curvature, random walk on a metric space.
Mots-clés : transportation distance 
@article{MZM_2016_100_4_a10,
     author = {O. V. Rubleva},
     title = {The {Ricci} {Curvature} of a {Weighted} {Tree}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {586--596},
     publisher = {mathdoc},
     volume = {100},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a10/}
}
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O. V. Rubleva. The Ricci Curvature of a Weighted Tree. Matematičeskie zametki, Tome 100 (2016) no. 4, pp. 586-596. http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a10/