One-sided sharp thresholds for homology of random flag complexes
Algebraic Topology
2024-02-28 v2 Combinatorics
Probability
Abstract
We prove that the random flag complex has a probability regime where the probability of nonvanishing homology is asymptotically bounded away from zero and away from one. Related to this main result we also establish new bounds on a sharp threshold for the fundamental group of a random flag complex to be a free group. In doing so we show that there is an intermediate probability regime in which the random flag complex has fundamental group which is neither free nor has Kazhdan's property (T).
Keywords
Cite
@article{arxiv.2108.04299,
title = {One-sided sharp thresholds for homology of random flag complexes},
author = {Andrew Newman},
journal= {arXiv preprint arXiv:2108.04299},
year = {2024}
}
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23 pages