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

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - O. V. Rubleva
TI  - The Ricci Curvature of a Weighted Tree
JO  - Matematičeskie zametki
PY  - 2016
SP  - 586
EP  - 596
VL  - 100
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a10/
LA  - ru
ID  - MZM_2016_100_4_a10
ER  - 
%0 Journal Article
%A O. V. Rubleva
%T The Ricci Curvature of a Weighted Tree
%J Matematičeskie zametki
%D 2016
%P 586-596
%V 100
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2016_100_4_a10/
%G ru
%F MZM_2016_100_4_a10
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/

[1] A. Besse, Mnogoobraziya Einshteina, Mir, M., 1990 | MR

[2] G. Perelman, The Entropy Formula for the Ricci Flow and Its Geometric Applications, 2002, arXiv: 0211159

[3] G. Perelman, Ricci Flow with Surgery on Three-Manifolds, 2003, arXiv: 0303109

[4] D. Bakry, M. Emery, “Diffusions hypercontractives”, Seminaire de Probabilites, 1123, Lecture Notes in Math., Berlin, 1985, 177–206 | MR | Zbl

[5] Y. Ollivier, “Ricci curvature of Markov chains on metric spaces”, J. Funct. Anal., 256:3 (2009), 810–864 | DOI | MR | Zbl

[6] Fan Chung and S.-T. Yau, “Logarithmic Harnack inequalities”, Math. Res. Lett., 1996, 793–812 | MR

[7] Y. Lin, L. Y. Lu and S. T. Yau, “Ricci curvature of graphs”, Tohoku Math. J., 63 (2011), 605–627 | DOI | MR | Zbl

[8] L. V. Kantorovich, “O peremeschenii mass”, Teoriya predstavlenii, dinamicheskie sistemy. XI, Spetsialnyi vypusk, Zap. nauchn. sem. POMI, 312, POMI, SPb., 2004, 11–14 | MR | Zbl

[9] A. O. Ivanov, A. A. Tuzhilin, “Odnomernaya problema Gromova o minimalnom zapolnenii”, Matem. sb., 203:5 (2012), 65–118 | DOI | MR | Zbl

[10] L. Euler, “The Kenigsberg bridges”, Sci. Amer., 1953, 66–70 | DOI