Integral Homology of Random Simplicial Complexes

Tomasz Łuczak*, Yuval Peled

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


The random 2-dimensional simplicial complex process starts with a complete graph on n vertices, and in every step a new 2-dimensional face, chosen uniformly at random, is added. We prove that with probability tending to 1 as n→ ∞, the first homology group over Z vanishes at the very moment when all the edges are covered by triangular faces.

Original languageAmerican English
Pages (from-to)131-142
Number of pages12
JournalDiscrete and Computational Geometry
Issue number1
StatePublished - 1 Jan 2018

Bibliographical note

Funding Information:
Acknowledgements This work was carried out when TŁ visited the Institute for Mathematical Research (FIM) of ETH Zürich. He would like to thank FIM for the hospitality and for creating a stimulating research environment. TŁ partially supported by NCN Grant 2012/06/A/ST1/00261. YP is grateful to the Azrieli foundation for the award of an Azrieli fellowship.

Publisher Copyright:
© 2017, Springer Science+Business Media, LLC.


  • Hitting time
  • Homology Shadow
  • Random simplicial complexes


Dive into the research topics of 'Integral Homology of Random Simplicial Complexes'. Together they form a unique fingerprint.

Cite this