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Betti numbers of random manifolds
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Farber, Michael and Kappeler, Thomas (2008) Betti numbers of random manifolds. Homology, Homotopy and Applications, Vol.10 (No.1). pp. 205-222. ISSN 1532-0073.
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Official URL: http://www.intlpress.com/HHA/
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 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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | Homology, Homotopy and Applications | ||||
Publisher: | International Press | ||||
ISSN: | 1532-0073 | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.10 | ||||
Number: | No.1 | ||||
Page Range: | pp. 205-222 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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