Geodesic
Limit theorems for Betti numbers of random simplicial complexes
Homology, homotopy, and applications, Tome 15 (2013) no. 1, pp. 343-374.

Voir la notice de l'article provenant de la source International Press of Boston

There have been several recent articles studying homology of various types of random simplicial complexes. Several theorems have concerned thresholds for vanishing of homology groups, and in some cases expectations of the Betti numbers; however, little seems known so far about limiting distributions of random Betti numbers. In this article we establish Poisson and normal approximation theorems for Betti numbers of different kinds of random simplicial complexes: Erdös-Rényi random clique complexes, random Vietoris-Rips complexes, and random Cech complexes. These results may be of practical interest in topological data analysis.
DOI : 10.4310/HHA.2013.v15.n1.a17
Classification : 05C80, 60D05
Keywords: random graph, topological data analysis, central limit theorem, random simplicial complex 
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     title = {Limit theorems for {Betti} numbers of random simplicial complexes},
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Matthew Kahle; Elizabeth Meckes. Limit theorems for Betti numbers of random simplicial complexes. Homology, homotopy, and applications, Tome 15 (2013) no. 1, pp. 343-374. doi : 10.4310/HHA.2013.v15.n1.a17. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2013.v15.n1.a17/

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