When does the top homology of a random simplicial complex vanish?

Lior Aronshtam*, Nathan Linial

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


Several years ago Linial and Meshulam (Combinatorica 26 (2006) 457-487) introduced a model called Xd(n,p) of random n-vertex d-dimensional simplicial complexes. The following question suggests itself very naturally: What is the threshold probability p=p(n) at which the d-dimensional homology of such a random d-complex is, almost surely, nonzero? Here we derive an upper bound on this threshold. Computer experiments that we have conducted suggest that this bound may coincide with the actual threshold, but this remains an open question.

Original languageAmerican English
Pages (from-to)26-35
Number of pages10
JournalRandom Structures and Algorithms
Issue number1
StatePublished - 1 Jan 2015

Bibliographical note

Publisher Copyright:
© 2013 Wiley Periodicals, Inc.


  • Collapsibility
  • Homology
  • Random simplicial complex
  • Threshold
  • Topology


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