Integral Homology of Random Simplicial Complexes

Tomasz Łuczak; Yuval Peled

doi:10.1007/s00454-017-9938-z

Integral Homology of Random Simplicial Complexes

Tomasz Łuczak, Yuval Peled

The Hebrew University of Jerusalem

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	131-142
Number of pages	12
Journal	Discrete and Computational Geometry
Volume	59
Issue number	1
DOIs	https://doi.org/10.1007/s00454-017-9938-z
State	Published - 1 Jan 2018

Keywords

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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10.1007/s00454-017-9938-z

Cite this

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title = "Integral Homology of Random Simplicial Complexes",

abstract = "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.",

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KW - Random simplicial complexes

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JO - Discrete and Computational Geometry

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Integral Homology of Random Simplicial Complexes

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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