When does the top homology of a random simplicial complex vanish?
Combinatorics
2012-03-16 v1
Abstract
Several years ago Linial and Meshulam introduced a model called X_d(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.
Keywords
Cite
@article{arxiv.1203.3312,
title = {When does the top homology of a random simplicial complex vanish?},
author = {L. Aronshtam and N. Linial},
journal= {arXiv preprint arXiv:1203.3312},
year = {2012}
}