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Matematicheskie Zametki, 2016, Volume 100, Issue 4, Pages 586–596
DOI: https://doi.org/10.4213/mzm10810 (Mi mzm10810) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The Ricci Curvature of a Weighted Tree

O. V. Rubleva

Lomonosov Moscow State University
Full-text PDF (457 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm10810
Abstract: 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, transportation distance, random walk on a metric space.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation НШ-581.2014.1
Russian Foundation for Basic Research 13-01-00664а
This work was supported by the Russian Foundation for Basic Research under grant 13-01-00664a and by the program “Leading Scientific Schools” under grant NSh-581.2014.1.
Received: 08.06.2015
English version:
Mathematical Notes, 2016, Volume 100, Issue 4, Pages 597–606
DOI: https://doi.org/10.1134/S0001434616090315
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: O. V. Rubleva, “The Ricci Curvature of a Weighted Tree”, Mat. Zametki, 100:4 (2016), 586–596; Math. Notes, 100:4 (2016), 597–606
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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