Integral Homology of Random Simplicial Complexes

Tomasz Łuczak, Yuval Peled

Research output: Contribution to journalArticlepeer-review


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


  • Hitting time
  • Homology Shadow
  • Random simplicial complexes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics


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