PreprintCC BY 4.0arXiv
Property (T) for random groups in the density model with d > 1/4
Abstract
We prove that random groups in the Gromov density model (under a certain divisibility condition) have property (T) asymptotically almost surely for any density d > 1/4. This established 1/4 as the threshold for property (T), since it was shown by Ashcroft that they do not have property (T) for d < 1/4.
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BibTeX
@misc{oppenheim2026property,
title = {{Property (T) for random groups in the density model with $d > \frac14$}},
author = {Izhar Oppenheim},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.21255},
eprint = {2609.21255},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.21255},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Property (T) for random groups in the density model with d > 1/4
AU - Izhar Oppenheim
PY - 2026
DA - 2026/09/18
PB - arXiv
DO - 10.48550/arxiv.2609.21255
UR - https://arxiv.org/abs/2609.21255
AB - We prove that random groups in the Gromov density model (under a certain divisibility condition) have property (T) asymptotically almost surely for any density d > 1/4. This established 1/4 as the threshold for property (T), since it was shown by Ashcroft that they do not have property (T) for d < 1/4.
ER -