Geodesic
Discrete Curvature and Abelian Groups
Canadian journal of mathematics, Tome 68 (2016) no. 3, pp. 655-674

Voir la notice de l'article provenant de la source Cambridge

DOI

We study a natural discrete Bochner-type inequality on graphs, and explore its merit as a notion of “curvature” in discrete spaces. An appealing feature of this discrete version of the so-called ${{\Gamma }_{2}}$ -calculus (of Bakry-Émery) seems to be that it is fairly straightforward to compute this notion of curvature parameter for several specific graphs of interest, particularly, abelian groups, slices of the hypercube, and the symmetric group under various sets of generators. We further develop this notion by deriving Buser-type inequalities (à la Ledoux), relating functional and isoperimetric constants associated with a graph. Our derivations provide a tight bound on the Cheeger constant (i.e., the edge-isoperimetric constant) in terms of the spectral gap, for graphs with nonnegative curvature, particularly, the class of abelian Cayley graphs, a result of independent interest.
DOI : 10.4153/CJM-2015-046-8
Mots-clés : 53C21, 57M15, Ricci curvature, graph theory, abelian groups 
Klartag, Bo'az; Kozma, Gady; Ralli, Peter; Tetali, Prasad. Discrete Curvature and Abelian Groups. Canadian journal of mathematics, Tome 68 (2016) no. 3, pp. 655-674. doi: 10.4153/CJM-2015-046-8
@article{10_4153_CJM_2015_046_8,
     author = {Klartag, Bo'az and Kozma, Gady and Ralli, Peter and Tetali, Prasad},
     title = {Discrete {Curvature} and {Abelian} {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {655--674},
     year = {2016},
     volume = {68},
     number = {3},
     doi = {10.4153/CJM-2015-046-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-046-8/}
}
TY  - JOUR
AU  - Klartag, Bo'az
AU  - Kozma, Gady
AU  - Ralli, Peter
AU  - Tetali, Prasad
TI  - Discrete Curvature and Abelian Groups
JO  - Canadian journal of mathematics
PY  - 2016
SP  - 655
EP  - 674
VL  - 68
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-046-8/
DO  - 10.4153/CJM-2015-046-8
ID  - 10_4153_CJM_2015_046_8
ER  - 
%0 Journal Article
%A Klartag, Bo'az
%A Kozma, Gady
%A Ralli, Peter
%A Tetali, Prasad
%T Discrete Curvature and Abelian Groups
%J Canadian journal of mathematics
%D 2016
%P 655-674
%V 68
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2015-046-8/
%R 10.4153/CJM-2015-046-8
%F 10_4153_CJM_2015_046_8

Cité par Sources :