Geodesic
Betti numbers of random manifolds
Homology, homotopy, and applications, Tome 10 (2008) no. 1, pp. 205-222.

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

We study mathematical expectations of Betti numbers of configuration spaces of planar linkages, viewing the lengths of the bars of the linkage as random variables. Our main result gives an explicit asymptotic formulae for these mathematical expectations for two distinct probability measures describing the statistics of the length vectors when the number of links tends to infinity. In the proof we use a combination of geometric and analytic tools. The average Betti numbers are expressed in terms of volumes of intersections of a simplex with certain half-spaces.
DOI : 10.4310/HHA.2008.v10.n1.a8
Classification : 55R80
Keywords: linkage, polygon space, random linkage, Betti number 
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Michael Farber; Thomas Kappeler. Betti numbers of random manifolds. Homology, homotopy, and applications, Tome 10 (2008) no. 1, pp. 205-222. doi : 10.4310/HHA.2008.v10.n1.a8. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2008.v10.n1.a8/

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