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Topology of random linkages
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Farber, Michael (2008) Topology of random linkages. Algebraic & Geometric Topology, Vol.8 (No.1). pp. 155-171. doi:10.2140/agt.2008.8.155 ISSN 1472-2747.
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Official URL: http://dx.doi.org/10.2140/agt.2008.8.155
Abstract
Betti numbers of configuration spaces of mechanical linkages (known also as polygon spaces) depend on a large number of parameters – the lengths of the bars of the linkage. Motivated by applications in topological robotics, statistical shape theory and molecular biology, we view these lengths as random variables and study asymptotic values of the average Betti numbers as the number of links n tends to infinity. We establish a surprising fact that for a reasonably ample class of sequences of probability measures the asymptotic values of the average Betti numbers are independent of the choice of the measure. The main results of the paper apply to planar linkages as well as for linkages in R3. We also prove results about higher moments of Betti numbers.
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: | Algebraic & Geometric Topology | ||||
Publisher: | Mathematical Sciences Publishers | ||||
ISSN: | 1472-2747 | ||||
Official Date: | 8 February 2008 | ||||
Dates: |
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Volume: | Vol.8 | ||||
Number: | No.1 | ||||
Page Range: | pp. 155-171 | ||||
DOI: | 10.2140/agt.2008.8.155 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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