Betti numbers of random manifolds

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dc.creatorFarber, Michael
dc.creatorKappeler, Thomas
dc.date2007-03-30
dc.date.accessioned2026-07-07T07:55:08Z
dc.date.available2026-07-07T07:55:08Z
dc.descriptionWe 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.
dc.identifierhttps://arxiv.org/abs/math/0703929
dc.identifierhttp://arxiv.org/abs/math/0703929
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/126863
dc.subjectAlgebraic Topology
dc.subjectProbability
dc.titleBetti numbers of random manifolds
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