Year: 2026
Type: preprint
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 $d > \frac{1}{4}$. This established $\frac{1}{4}$ as the threshold for property (T), since it was shown by Ashcroft that they do not have property (T) for $d < \frac{1}{4}$.
Source: arXiv (Cornell University)
Author: Oppenheim, Izhar
Institution: Ben-Gurion University of the Negev
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213891841