The threshold for integer homology in random d-complexes
Algebraic Topology
2014-04-11 v2 Combinatorics
Probability
Abstract
Let Y ~ Y_d(n,p) denote the Bernoulli random d-dimensional simplicial complex. We answer a question of Linial and Meshulam from 2003, showing that the threshold for vanishing of homology H_{d-1}(Y; Z) is less than 80d log n / n. This bound is tight, up to a constant factor.
Cite
@article{arxiv.1308.6232,
title = {The threshold for integer homology in random d-complexes},
author = {Christopher Hoffman and Matthew Kahle and Elliot Paquette},
journal= {arXiv preprint arXiv:1308.6232},
year = {2014}
}
Comments
12 pages, updated to include an additional torsion group bound