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Betti numbers of random manifolds


Farber, M; Kappeler, T (2008). Betti numbers of random manifolds. Homology, Homotopy and Applications, 10(1):205-222.

Abstract

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 formula 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.

Abstract

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 formula 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.

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Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Mathematics (miscellaneous)
Language:English
Date:2008
Deposited On:26 Feb 2009 07:14
Last Modified:25 Jun 2022 20:50
Publisher:International Press
ISSN:1532-0073
OA Status:Hybrid
Publisher DOI:https://doi.org/10.4310/HHA.2008.v10.n1.a8
Related URLs:http://www.ams.org/mathscinet-getitem?mr=2386047
http://arxiv.org/abs/math/0703929v1
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