The threshold function for vanishing of the top homology group of random $d$-complexes

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dc.creatorKozlov, Dmitry N.
dc.date2009-04-10
dc.date.accessioned2026-07-07T13:02:25Z
dc.date.available2026-07-07T13:02:25Z
dc.descriptionFor positive integers $n$ and $d$, and the probability function $0\leq p(n)\leq 1$, we let $Y_{n,p,d}$ denote the probability space of all at most $d$-dimensional simplicial complexes on $n$ vertices, which contain the full $(d-1)$-dimensional skeleton, and whose $d$-simplices appear with probability $p(n)$. In this paper we determine the threshold function for vanishing of the top homology group in $Y_{n,p,d}$, for all $d\geq 1$.
dc.identifierhttps://arxiv.org/abs/0904.1652
dc.identifierhttp://arxiv.org/abs/0904.1652
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/226442
dc.subjectAlgebraic Topology
dc.subjectProbability
dc.subject55U10; 60B99
dc.titleThe threshold function for vanishing of the top homology group of random $d$-complexes
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