Homological connectivity of random 2-complexes

Nathan Linial*, Roy Meshulam

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

177 Scopus citations

Abstract

Let Δ n-1 denote the (n - 1)-dimensional simplex. Let Y be a random 2-dimensional subcomplex of Δ n-1 obtained by starting with the full 1-dimensional skeleton of Δ n-1 and then adding each 2-simplex independently with probability p. Let H 1(Y;2) denote the first homology group of Y with mod 2 coefficients. It is shown that for any function ω(n) that tends to infinity limn →∞ Prob[H1(Y;double-struck F sign2) = 0{0 p = 2 log n-w(n)/n 1 p = 2 log n+w(n)/n.

Original languageAmerican English
Pages (from-to)475-487
Number of pages13
JournalCombinatorica
Volume26
Issue number4
DOIs
StatePublished - Aug 2006

Bibliographical note

Funding Information:
* Supported by an Israel Science Foundation grant.

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